Transcript for:
JEE 2025 Preparation Lecture Overview

good morning good morning good morning and very happy Pongal Makar sankranti happy Lori to all the Jay Warriors who are preparing for the 2025 January attempt I know it's a time where many of the families your you know closed ones will gather together to celebrate but you know uh for the circumstances you are in you have to utilize this particular holiday uh you know by studying properly and making sure that you utilize every single minute yes there will be a time where you'll be celebrating these festivals next year in the IIT campus in the NIT campus in the bits campus and that is the time when you will feel very proud that you last year were very very particular and focused on your J M's January attempt all right so let's begin and uh let's start with the complete physics one short marathon with the concept and the questions many of them will be pyqs or your uh most important models of question so I'll be revising the concept I'll be going through the concept and then we will be doing the models of question based on that particular concept obviously we will be taking up only the high weightage important Concepts there are many many Concepts throughout the 11th and 12th standard syllabus so you can expect around close to 100 Concepts that we'll be doing today in this particular session it is going to be a long Marathon I'll be giving a break after some time so be ready for it okay so my name is Captain stas your physics Master teacher and I have been you know guiding mentoring teaching kids for more than 13 years now and thousands of my students are right now in iits and many of them are also in nits bits and you name it this year obviously it's your turn I need to make sure that my kids in 2025 are cracking the J examination no matter what and because you are attending this particular lecture it's my responsibility to ensure I give you all those kind of questions which will come in the examination so quickly smash this like button and subscribe to the number one J English Channel in the country all right so let's begin hi only J welcome vet hi kesan an welcome anandu hi Hitman C subba study vetri welcome harboran hi sish hi welcome welcome Padu welcome nikil nice to see you all hello Arjun Hello Lord hello Sigma Institute awaria nice to see you w come and namaskaram yes uh welcome welcome aboard namaskar all right let's begin first let's start with the concept we are going with the 11th standard chapters first then we will go to the 12th standard chapters that's how the flow will be and we are going almost sequentially right from units Dimensions kinematics then your are Newton's Laws work Energy Center of mass that's how the flow will be homogeneity principle remember is a principle which equates the dimensions on both sides now you might be wondering what the hell is Dimensions or you might have forgotten let's revise that and the concept of dimensions and dimension analysis is first of all in the homogeneity principle and also to check the correctness of equation and also to derive certain things so let's understand one thing that there is a clear-cut difference between units and dimensions units and dimensions like say for example if I take the quantity of let's say you know Mass if the physical quantity that I take is mass then the unit of mass can be kg can be gram it can be let's say milligram or it can be ton okay all these things are nothing but the units different manners in which you can measure the mass but dimensionally Mass is measured like this it is written down in square brackets and dimensional formula is basically M similarly you can talk about length length length can be also measured in different ways like feet ctim kilometer meter Etc but dimensionally it is having the formula L similarly if I write speed or velocity speed and velocity I can measure it in kilometers per hour cm per second or basically miles miles per minute or basically meters per second but dimensionally the formula will be because kilometers centimeters they are all lengths and Below you have time so it is l t to1 l / T which is negative power of T So a quantity may have multiple units but it will have an unique Dimension all right also sometimes it can happen that two quantities have the same Dimension but they have different units example example if I tell you work work and torque work and torque the dimension formula is the same which is M to 1 L ra to 2 and you have basically T ra to minus 2 so basically they have the same dimensions they have the same dimensions but you will notice that their units are different units are different units are going to be different for work it is measured in jewels and torque is measured in Newton meter okay so sometimes some physical quantities may have same Dimension but their units could be they are measured in different units altogether similarly also keep in mind there are certain physical quantities which do not have Dimensions yet they have units for example if I give you angle angle what's the dimensional formula for angle it is basically dimensionless it is basically Dimension less but it has a unit it can be measured in radian or it can be measured in basically degree there are some quantities which neither have units nor do they have dimensions for example like say refractive index refractive index or coefficient of friction right all these physical quantities there is no unit there is no unit for refractive index nor do they have any Dimensions is this now very clear the difference between units and dimensions never ever get confused yep trigonometric function strain correct awesome no we are not doing derivations over here yep so now that you understand this you should also remember that whenever I put an equal to symbol over here then whatever quantities are there on the left hand side and whatever quantities are there on the right hand side dimensionally they should be equal so whatever I write over here and whatever I write over here dimensional formulas should be the same even if I add something or even if I subtract something their Dimensions must be same must be same during during during what addition and subtraction when you do multiplication or division multiplication or division all right is equal to some Dimension or let's say this thing divided by this thing is equal to this then in these cases the dimensions the dimensions of each quantity of each quantity may be different may be different that is perfectly okay like for example this is M to 1 L and this is l 1 into tus1 so dimensionally M will be coming over here check this out what will happen over here this will be nothing but M ra to one L into L will become l squ p to minus one will come over here as it is each of the quantities can have different dimensions no harm in that if this is M ra to one and this is let's say t ra to one this can be then you know probably M to 1 T to minus one so multiplication division is done normally like the nor normal rules of multiplication division each quantity can be different dimensionally only while addition and subtraction the dimensions should be equal that is basically your principle of homogeneity also every term in the physical quantity must have the same Dimension which we already discussed this is also used to check if an equation is correct or to derive unknown relation remember one thing that if by chance it happens the dimensions on this side is not equal to the dimensions on this side then dimensionally dimensionally it is not correct dimensionally it is not correct and physics wise also it is going to be not correct physics wise also it is not going to be correct okay 100% if the dimensions don't match you can eliminate such options what you can do this can be used to eliminate this can be used to eliminate certain op in certain cases especially in your objective examination now this principle can also be used to derive certain relationships say for example I know that say for example some physical quantity depends on physical quantity one physical quantity two physical quantity three okay then I don't know how is it exactly related so you will start by assuming okay this physical quantity is some constant into P1 ra to X P2 ra to Y and some physical quantity raised to zed if more quantities are there more variables can be assumed accordingly then you will say okay so that's why dimensions of P constant is always this is going to be a dimensionless quantity okay so then this will be basically P1 Dimension raed to X p2's Dimension raised to Y and P3 is dimension raised to Z so solving this you will get the value of x y and z by comparison by comparing by comparing the left hand side with the rhs right hand side you will see what is the dimensions here of mass and what is the dimension here for mass for length for time Etc and comparing them you will be able to derive the formula for that particular relationship yep I hope this is clear yes awesome so let's let's basically do some questions on this here is a first question test if this particular formula is it dimensionally correct like it can come as a statement based question maybe it is statement one or it can be like an option it is not correct mathematically but physics wise it is correct or it is not it is uh it is not correct at all or it is correct mathematically and physically also so all such options can come so let's see whether it is correct or wrong dimensional formula is this correct or wrong come on my dear students now first of all if you check the left hand side the left hand side which is basically T the dimension of it is nothing but just time so time raised to one similarly if you check the dimensional formula of the right hand side which is basically 2 Pi root of mass / Force by X well dimensionally this will be dimensions of 2 pi dimensions of 2 pi into dimensions of mass raised to Half Upon the dimension of force raised to half and X is going to go on the top so X is the dimension raised to half technically speaking 2 pi is the dimension less mass is M raed to 1 so raised to half X is basically length so length raised to one whole thing raised to half Force has a dimension of M to 1 L ra to 1 T ra to minus 2 the whole thing raised to half everything is raised to half mm cancels l l will cancel so the only thing remaining by the way this is dimensionless so don't worry about it this goes on the top it will become T ra to 2 the whole thing raised to half which is basically T which is the same as the dimensions on the left hand side so hence as you can see this right hand side and left hand side dimensions are equal hence dimensionally dimensionally it is correct dimensionally it is definitely correct nothing wrong if you check formula wise also there is nothing wrong you will see 2 Pi root of M by force is nothing but KX spring force is nothing but KX divided by X XX cancels so this will become 2 pi under root M by K which is actually the time period which is actually the time period of oscillation so yes formula wise also it is correct there is nothing wrong in it formula wise also there is nothing wrong happy Pongal to you hi Jeffrey y all right exactly B that's what we are doing we are doing the concept then the pyqs concept pyq that's what we are doing all right next question on your screen it says that the speed of a wave is produced in water which is given by velocity is some Lambda Lambda and row are the wavelength and the acceleration due to gravity and this is nothing but the density of that liquid what is the value of a b c respectively in this particular equation okay the duration of this live might be 4 to 6 hours anywhere in between that or even more I don't know we're just going with the flow so keep a mindset of 5 hours to 6 hours or 4 hours so that way you are mentally prepared okay now first of all on the left hand side you just have velocity on the right hand side you have basically Lambda so Lambda raised to a and then gravitational acceleration raised to B and then density raised to C dimensionally both of them should be equal what is the dimensional formula for velocity because it is me/ second so it will be length per unit time L1 tus one wavelength it is length so L ra to 1 ra to a acceleration due to gravity meters that means length per second square that means T to minus 2 ra to B density mass per volume mass is M to 1 volume is L Cub but below so L Cube will be minus 3 l Cub will be minus 3 okay so that is what it is now solve the right hand side properly so you have L ra to a l ra to B and and L to minus 3 C then Mass wise you have M to just C and time wise you just have t to minus 2B is that right length is there Mass is taken care of time is only there over here and on the left hand side L rais to one in fact mass is not there only if you notice so it is technically M to 0 L ra to 1 T to minus1 now start comparing start comparing Mass's power Mass's power on the left hand side is zero here the Mass's power is C so basically C is zero one thing done next check for length or check for maybe time so time power is1 here the power is basically -2b so minus minus cancels so 2 B is equal to 1 therefore B is basically half lastly check the power for length on both sides left hand side it is one right hand side it is a + b - 3 C okay a I think I have to find out B value is nothing but half C value was nothing but zero okay so therefore a will be 1 minus half which is basically again half so a will be half B will be half c will be zero which is option number c which is nothing but option number c got it my dear Warriors everybody with me that is how you solve these dimensional based questions have you now Got Confidence everyone with me yep uh game gamer Creator most of the chapters are going to be covered but in those chapters only those important Concepts like if a chapter has uh let's say chapter number X has let's say seven Concepts but every year we see that for sure these two concepts will come then those two concepts I will be doing over here because we are concentrating on marks now not concentrating on covering the syllabus the concentration is on marks what if I tell you I will give you marks I am not interested in just covering the syllabus for the sake of it because then you are unnecessarily doing something which is not required do what is required what is required marks if I tell you I'll give you marks or I will give you full syllabus what you want but if you do full syllabus you might take a lot of time you might not be able to complete it you might not do it completely properly and your marks might be maybe 60 or 70 percentile but if I tell you no I'll give you 99 percentile maybe complete syllabus not done some chapters or some topics are left out you will get 95 98 99 percentile obviously you will choose that option where you get more marks right correct awesome right let's move on let's move on to the next concept of screw gauge and basically that concept of least count and how do you measure those uh things in screw gauge now screw gauge is remember a device where you rotate rotate the screw till it touches and it gets a click sound and you stop there and you make those readings based on the markings on the screw and you measure the length of the device usually used to measure the diameter of a ball or the width of something or the sheet thickness stuff like that it has a very good accuracy generally better than the wer caliper so a screw gauge will have a rotating screw it will have a circular scale so there is always is a circular scale which has some markings so that is why it has circular scale reading and as that screw rotates that circular scale will allow that big Rod inside of it to move that Rod will have some markings and that is the main scale which goes left right the circular scale will go round and round circular scale reading it will have the rod will move back and forth till it touches the object that has the main scale the rod will not rotate it will just move back and forth okay that's like the screw all right so that has the main scale over it now there is something called as the pitch of a screw gauge pitch is nothing but how much does it move per rotation so when I rotate it once how much does that Rod move back and forth is called as the pitch so for one rotation If It Moves 0.5 mm then the pitch is5 mm if I rotate it 10 times then it rotate moves by 2 mm so for 10 rotation it moves by 2 mm so per rotation it will move by 2 ided 10 which is2 mm so then the pitch is.2 mm per rotation how much does it move is called as the pitch distance mov upon the number of rotations that's how it works this pitch is important for the calculation of something called as the least count now least count is basically the smallest measurement that you can make by any particular device normally your watch that you wear has a least count of 1 second usually the um you know the weighing machines that are there around you usually they have a least count of one gram then if you talk about a normal scale it has a least count of 1 mm a screw gauge usually a standard screw gauge usually has a least count of 01 mm yes 01 mm remember 1 mm for a meter scale 01 for a screw gauge 0.1 is for a wer caliper so meter scale is not that great verer caliper is slightly better screw gauge is the best because very small error in it because the least count is 0.1 millimet that's very very small so what is the least count the least count is whatever pitch you find divided by remember that circular scale the C cular scale will have some markings so number of markings on the circular scale you just divide the pitch with it so if it had 100 divisions divide the pitch with 100 that is the least count of the circular scale so say for example the distance moved by it was 2 mm for let's say 10 rotations then the pitch will be 2 divided by 10 which is2 mm let's say now once I got the pitch as .2 mm let's say the number of Divisions on the circular scale were example 20 there were 20 lines on the circular scale so 0. 2 divided by 20 2 two cancels so it will be 0.1 divided 10 which is nothing but 01 mm so the least count of that screw gauge will be 01 mm is that okay how you do these calculations everybody with me yes awesome now now uh yes we are doing as many things as possible deu don't worry and I will want to keep it as one short because then if I do it in two three lectures third lecture nobody comes yeah they're like oh sir I first have to complete first lecture I will do it concisely and I will do all the important things don't worry this is a complete physics Marathon now once you get the least count the final answer that you get the reading that you get is given by the total reading is given by this formula the first thing in it is in the MSR MSR is the main scale reading remember that Rod which moves back and forth on that scale what is that reading that you get which line are you just able to see that is your main scale Reading Plus least count which we just figured out over here that same least count you put over here multiplied by the circular scale reading remember on that Circle when you rotate and you stop because the Ro is just touching the object on the circle whatever reading you get that becomes the circular scale reading so circular scale reading into the least count plus the main scale the rod which moves that is your total reading of the micrometer screw by the way the formula for verier caliper is also very similar instead of circular scale reading you multiply the least count with verar scale reading and here you still have main scale reading that's all it's the same it's not very different that you get and instead of actually least count you have basically something called as a verar scale sorry least count is there instead of circular scale that verar scale reading which you get is actually the digit of coincidence which verar scale reading coincides that's what you multiply it okay now sometimes these machines these instruments have a zero error in it meaning when no object is placed still it is showing some reading now there are two kinds of errors that you can get one is a positive error and one is a negative error positive error is when nothing is kept imagine you have a weighing machine and nothing is kept still it is showing 10 grams so when you actually put something and it shows 60 grams so you will think oh when nothing was there still it was showing 10 now it is showing 60 so 60 is not the correct Mass so I have to take out 10 G so when it is already showing plus 10 G it's a positive error and a positive error always has to be subtracted because it is showing an excess value it is not correct so you subtract it that is what you do for a positive error when there is a negative error meaning when there is nothing kept on the pan it is showing minus 10 G when you keep an object it shows 60 G you'll think if it was showing minus 10 when nothing was kept then it reaches zero then it climbs to 60 that means the actual mass will be 10 + 60 oh so when there is a negative error you add that negative error got it so negative error means it is showing less so you have to compensate it by adding it is that right okay so the corrected reading will be the total reading minus or plus that zero error that's all all right now let's do a question based on this there is a screw gauge read the question properly Now read the question properly everyone come on my dear students read the question what is the the screw gauge has 100 divisions on the circular scale main scale moves by5 mm on one rotation the zero of the scale lies between uh six divisions below the line of the graduation when the two studs are brought in contact when you place some object four linear scale divisions are visible will the 46 division on the scale is coinciding so the diameter of the virus okay first go by Basics guys first go by Basics what is given over here first let's do the calculations for the pitch all right it moves by5 mm on one complete rotation that means basically the pitch is .5 mm what is the least count I had told you it is nothing but the pitch divided by circular scale divisions which means it is .5 mm upon how many divisions are there it is 100 so 100 divisions so therefore the least count therefore the Le East count will be nothing but 0.5 mm is that right 0.5 there are 100 divisions on the circular scale and the main scale moves by .5 mm on one complete rotation is that right everyone with me on this perfect yep all right welcome Alvin yes kimch maama thank you Lisa all right yes the PDF will be uploaded B4 after a day yeah today it might not be possible okay tomorrow because today everybody's on leave only sh s is working all the YouTube teachers are working out here okay just for you next thing is basically I think the zero error zero error is also there if you noticed there is something like zero error here the zero of the circular scale lies six divisions below the graduation when the studs are brought together studs are brought together contact with each other means there is nothing in nothing else kept in between the rod is just touching that part the stud of that screw gauge so it is still showing some reading so therefore there is some zero error over here now when you look at that zero error you should realize that the circular scale if this is what it is and this is your main scale it is mentioned that the zero of the circular scale lies six divisions below the zero of the circular scale lies six divisions below over here so that means this number is basically six so it is already showing six M six as the reading so it is definitely a positive error it is definitely a positive error because the zero is below six will be here so I have to subtract the answer later on so what is that zero error it will be main scale Reading Plus the least count multiplied by the circular scale reading the zero reading on the main scale is zero plus plus least count is nothing but 0.05 and what is the circular scale reading it is basically six so this is going to be oh sorry this was 05 my bad 05 into 6 05 into 6 05 into 6 5 6 are 30 guys so this will be nothing but 03 mm 03 mm everybody with me got it very good yeah so sir how the session would be Nya the session has already started you can already experience it all right next important thing is basically the reading that you get when you place with the object when you place it with the object so let's read this properly main scale Reading Plus least count multiplied by circular scale reading okay read it properly when a wire is placed four linear scale divisions are visible so four linear scale divisions are visible means linear scale means line line means that Rod the main scale so main scale reading is basically four plus plus okay now there is a catch over here there is a catch over here when if you see the question lot of you might think the main scale reading is four but actually that catch is if you complete a rotation if you complete a then the circular scale moves by 0.5 mm so that means each marking on that rod on that main scale is5 mm apart got it I hope this is clear when you rotate it once it is moving by 0.5 that means the it moves from one marking to the next marking again one rotation 100 divisions moves to the next marking moves to the next marking that means when the main scale reading is four remember two uh or rather I will say one division will be .5 mm One Division will be 0.5 mm so four divisions will be how many millimeters think about it four divisions will be 2 millim so the main scale value will be basically 2 mm is this clear lot of students usually make a silly mistake over here okay now the next important thing is the least count what is the least count we just got it to be 0.05 mm multiplied by circular scale reading circular scale reading was the 46th division on the circular scale so into basically 46 is this absolutely clear my dear students circular scale reading was already given to you so now just multiply this how much will it be 46 into 05 basically 46 into half 23 so guys point 23 23 everyone 23 so this will be nothing but 2 + 23 millim which is nothing but 2.23 mm but that should not be your final answer remember that our final answer will be 2.23 mm there is a positive zero error of how many millimeters .3 mm so I have to subtract it so hence it it will be 2.20 mm is this understood my dear Warriors is this understood yep okay so in this question I will tell you what exactly happens see the circular scale right that circular scale the total number of Divisions there were 100 divisions you rotate it once if you rotate it once what is happening that circular scale is moving by one division it is moving by one division from on that main scale the circular scale is moving how many millimeters it moved 0.5 millimet it is clearly mentioned .5 millim so basically it has moved from one division to the next Division and each division is basically .5 mm on the main scale on the main scale on the main scale so you rotate it once 100 divisions were there on the circular scale it moves by 0.5 mm so one division on the main scale is .5 mm is this clear okay so if I take 1 2 3 4 four divisions how much will be the length if I take four divisions if I take four divisions how much will be that length that length will be 2 mm so four divisions will be 2 mm that's why when the linear scale that means on the main scale if it shows fourth division that means it is actually speaking 2 mm understood yes is that absolutely clear Tamil yes everyone yeah okay this part is clear why the main scale reading is 2 mm how did I find that zero error I will say this again see this circular scale which was there it is clearly mentioned in the question that the zero of the scale is six divisions below the line of graduation when the studs are brought together that means when both the things are touching nothing is in between the zero of the circular scale is below the line of graduation means the main scale so if this is the main scale this is the main scale it is six divisions below it is six divisions below that means this is the number six this is the number six so ideally this zero should have been here but actually it is showing already some number that means if it is already showing some number that means it is a positive error how can it show some positive number that means you know it is not correct it has some zero error and it is a positive error understood why it is a positive error now why it is a positive error now it is clearly mentioned it is basically six divisions below the line of graduation I hope this is clear understood now clear give me a thumbs up if you guys got it give me a thumbs up if you guys got it awesome awesome yeah yes once I get it is six Mill whatever six divisions so once I know it is uh this number six will be the circular scale reading and probably the zero of the main scale will be here so therefore I will get my zero error from this particular formula main scale reading is zero plus circular scale reading is six least count is 0.05 understood that's how I get my zero error is this clear now everybody with me on this this concept also clear this kind of confusion usually they do specifically when the pitch is .5 mm specifically when the pitch is 0.5 mm okay what's the difference between pitch and least count pitch is basically when you rotate it once how much does it move but least count is even smaller than the pitch because when you rotate it once there were so many lines on the circular scale so when you're rotating you do one one tick or one you rotate it by one division on the circular scale then that that linear scale that Rod will move by a small amount that becomes the least count so so when you just do one pick on that circular scale the amount that it moves back or forth is the least count but when you rotate it one complete rotation how much it moves is basically the pitch that's the difference got it yeah yeah yes awesome okay okay samita let me tell you there there is a deliberate reason why I did not attach a picture reason being in the actual exam no picture will be there number one number to you have to you know make a rough diagram to understand it you cannot sit and draw a fair diagram if I sit and draw a fair diagram that's it time is gone so that's the reason why we have to sit with the rough diagrams to get the idea get the concept that's enough okay all right let me do another question and tell you okay by the way the for this the answer was I think 22 yes this is the correct answer let's say my dear students let's say another question another question let's try to do this let's say if I tell you the circular scale divisions are let's say 40 let's say the pitch let's say the pitch is let's say 2 mm okay then can you just figure out what is the least count for this uh particular screw Gage quickly come on everybody put it up in the chat box everybody put it up in the chat box let's build this question circular scale divisions are 40 pitch is 2 mm can you quickly find out the least count okay so the least count will be nothing but the pitch which is 2 mm the whole thing divided by 40 divisions so that's it 2x 40 is nothing but 1X 20 of a millimeter 1X 20 of a millimeter which is nothing but 0.05 mm so understand the difference when you have that circular scale you rotate it once it will exactly move it will move how many millimeters 2 mm it will move 2 mm from one division to the next division that is what it means it will basically move 2 mm understood how to calculate the least count perfect okay now let's say I already tell you let's say the least count is basically 0. 5 mm this is another fresh example let's say the least count is 05 mm example and I tell you and I tell you one Division One Division of that main scale main scale example each division is let's say 1 mm 1 millim or let's say I give you it is nothing but point point uh okay let's say it as 1 mm no problem let's say it is 1 mm all right each division on the main scale is EXA 1 mm now I tell you the main scale reading is let's say three and I tell you the circular scale reading is let's say for example uh 20 can you tell me what is the reading then can you tell me the reading of that particular screw gate can you tell me what is the reading then shown by the screw gaug let's do this question guys so what is the formula the formula is main scale Reading Plus the least count multiplied by multiplied by the circular scale reading what is the main scale Reading Main scale reading is basically three okay so three millimet each division is 1 one millimet so third division will be 3 mm perfect with that got it till this point okay least count what is the least count it is given to be 05 mm what is the circular scale reading it is basically 20 so this will be nothing but 3 + 3 + 05 into 20 1 Z goes with 1 decimal so 0.5 into 2 which is just going to be 1 so it will be basically 4 millim it will be basically just 4 mm everybody with me understood how the answer has to be found or awesome perfect this is how you need to do it let's say now it was given that there is a zero error let's say there is a zero error of given to be3 mm negative zero error of3 millimet negative what will you do so what will our final final answer be what will our final answer be think about it carefully the reading that we got was four but there is a negative error of3 so our final answer will it be 4 mm plus3 millimet or Min -.3 mm if there is a negative error you add it if there is a negative error you basically add that amount of uh negative error so the answer will be 4.3 mm that is your answer got it how this questions have to be solved it will be given in a text form you convert it into to this form what is main scale reading circular scale reading what is zero error what is the least count what is the pitch what is the number of Divisions if you do it like this you will definitely get the answer got it everyone awesome awesome let's proceed with the next concept of error combination now every measurement that you make every measurement that you make has some error so let's say there is a physical quantity let's let's say there is a physical quantity and that physical quantity is measured to be the value is M plus or minus Delta M this m is your most probable value this is your most probable measured value this is basically your absolute error this is your absolute error and then Delta M by m is then called as the relative error and then you also have Delta M by m multiplied by 100 which is then called as the percentage error of that particular reading so say for example I tell you the time that you have measured is 20 plus or minus 1 second so the absolute error in the measurement is 1 second the relative error in the measurement is 1 ided 20 which is nothing but 05 if you ask me the percentage error in this then that will be 1 by 20 multiplied by 100 which is basically 5% so there is a 5% error margin over here I hope this is clear everyone awesome till this point absolutely clear okay now there are different ways in which you can combine these errors there are different ways by which you can combine these errors so let let's see what are those error combinations possible say for example say for example you have length of a rod number one given to be two plus or minus or let's say 20 plus or minus 3 m or whatever another Rod is there whose length is let's say 40 plus or minus plus or minus let's say 2 m so if somebody asks you you're joining these rods together so that means the length will also be added so what is the total length what is the total length then what you do is you add the most probable values so 20 + 40 is going to be 60 plus or minus 60 plus or minus these things also should be added so it will become five so whenever you do addition you just add the most probable values and also the absolute errors now let's say there is another example where you you had certain mass given to be let's say 50 50 plus or minus uh let's say four and there is another Mass which is taken out from it which is let's say 10 plus or minus 10 plus or minus 2 now you are taking out something in this case you're taking out something so from Mass one you are taking out mass number two so what is the mass which basically remains this is basically subtraction of error how much mass is remaining just subtract the most probable value 50- 10 is 40 but never subtract this always add it so 4 + 2 is going to be six so whether you do addition or subtraction always remember this for for addition and subtraction the absolute errors errors are always always added are always added are always going to be added keep this in mind okay 3 + 2 4 + 2 always but this value or this values will always be added or subtracted depending on the sign over cool all right next important thing next important thing is multiplication division Etc how do you tackle this for tackling this multiplication division and any such thing remember always write the formula in the power form what do I mean by that for example kinetic energy kinetic energy is half MV s we know that so write it in the power form that means kinetic energy will be half Mass raised to One V to2 express everything in powers in the numerator another example let's say all right the speed of a wave is root of Young's modulus by density therefore V will be Young's modulus power is half density's power on the top if I write it it is negative half similarly some other question let's say see here things were multiplied here things were divided let's say you take another example maybe of U you know some random physical quantity it is dependent on some constant or let's say we take the force only electrostatic force kums constant charge one charge Char 1 charge 2 / r² so write it in the power form kums constant q1 to 1 Q2 ra to 1 and rus2 that is how you will first write it once you write it in that power form then what you do is to find the error in this quantity because this quantity and this quantity has error or there is some margin there is some problem here that is why this quantity has some error what you do is first write down the relative errors of everything what will you do first write down the relative errors of everything that means write Delta K by K then write Delta M by m then write Delta V by V okay here equal to is there put equal to if there is a constant forget it constants should not be worried about just take the powers what is the power of mass one multiply with it just take the powers and multiply with it it what is the power of velocity it is two so 2 into just add it this is the formula so if there is some error here and there is some error here this much error will be there here relatively so the relative errors are calculated not the absolute errors in addition subtraction you deal with absolute errors but in multiplication division and any other powers you tackle with relative errors so for example if this had say 5% error and let's say this had 2% error then 2 into .5 + 2% which is nothing but 1 + 2 so this will have 3% error so the kinetic energy percentage error will be 3% if velocity and mass had5 and 2% errors is this clear similarly over here what you do first write down all the relative errors velocity's relative error Young's modulus relative error and obviously the relative error of density obviously the relative error of density now put that equal to sign what is the power of young modulus half what is the power of density it is negative half so will you put negative half no don't put always put the mod value never ever put negative values always choose the positive values okay so that's how you do it similarly over here the relative error in force will be it is a constant so ignore it power of the charge is one so 1 into Delta q1 by q1 power of this charge is also 1 so Delta Q2 by Q2 power of R is 2 -2 but always take mod value so 2 * Delta R by R so that's how you combine errors for multiplication division roots or any such quantity got it yep everyone everybody with me yes now please remember one more thing that whatever formulas I have given over here please take a note this is only for small relative errors small relative errors typically less than 10% Like This is 2% 5% 6% 5% .9% 3% 4.2% then you can use this if it is not then you have no other option but to calculate both the values and then do it say for example I tell you uh say the k Energy Formula we know is half MV s and I tell you that listen the velocity is changed velocity is changed by example let's say 20% Then what is the kinetic energy Changed by then what is the change in that particular ktic energy you have no other option but to sit and calculate this how to sit and calculate I'll tell you if you talk about the initial conditions the kinetic energy was K the mass was M velocity was V this is the formula if you talk about the final values final values the velocity has been changed by 20% let's say it was increased let's say it was increased by 20% so final velocity the final velocity will be the old value of the Velocity plus that change which you did the old value was V the change was 20% so what is 20% of velocity 20% means 20 by 100 into V which is 1/ 15 1X 5 right this is V by 5 so this will be nothing but 6 V by 5 is that right final velocity will be 6 * V by 5 now what you do find the final kinetic energy which is half m v final Square which is half M final velocity is 6 V by 5 so 6 s v² by 5 S which is nothing but 36 by 25 * half M v² which is now the new kinetic energy so now in order to find the percentage change percentage change in the kinetic energy you find the new kinetic energy subtract it with the old kinetic energy divide it with the old kinetic energy and then multiply by 100 that is what is going to give me the answer so the new kinetic energy was nothing but 36 by 25 * half m v² is that right 36 by 25 * half M v² minus what was the old kinetic energy it was half M v² divided half M v² and then you just multiply this with 100 half MV sare half MV will cancel and you will get 36 by 25 - 1 36 by 25 - 1 the whole thing into 100 which is 36 - 25 into 100 this thing divided by 25 36 - 25 that's 11 into 25 and 100 goes four times so that is basically 44% that is the answer got it everyone no it is not 36% it is going to be 44% so when the errors are huge you have to go with that only for small relative errors you can use these formulas okay so let's do a question basically if length is this much breadth is this much what is L plus b what is basically L plus b come on very very straightforward question okay so how do we do this start by putting 2.33 1 and put Plus and put 2.1 over here there is nothing over here add both of them see what do you get this will be one this will be three this will be 4 and 2 + 2 is basically 4 4431 it is there over here but will you mark it definitely not you'll be like sir such a l question J will ask yes and many people will Mark a this is not correct be careful see whenever you add something or subtract something always check how many decimal places are there here there are three decimal places here there is one decimal place but our final answer is getting three decimal places which is wrong The Final Answer should have one decimal place because this is the least of the all always the least so then you have no other option but to round it off yes you will be rounding it off round it off round it off to to one decimal place which is the least decimal places what will it be check you have to get rid of this number 31 you have to get rid of this number 31 yes you have to get rid of this number 31 this number 31 you have to get rid of so when you write it down what will happen this will just become 4.4 this will just become 4.4 yes that is the rule when you add and subtract so in fact I can put it up here only also also The Final Answer also I'll put over here The Final Answer also when you add and subtract The Final Answer should have the least of decimal places not significant figures decimal places always The Final Answer should have least of the decimal places here there were no decimal places so need to break your head but if there were decimal points always least decimal value either addition or subtraction either addition or subtraction doesn't matter always least of the decimal place you'll be wondering sir how did I get rid of 31 like this sir if it was 71 will I still get rid of it no see there are two digits right two digits think in multiples of five 5 50 500 5,000 50,000 5 like that so two digit five number of power of 10 that is basically 50 if you compare the number 31 with 50 it is less than 50 so if it is less than the number 50 this is also twood digit this is also two digigit then you just write it down as it is the previous digit write it down as it is so hence 4.4 will be the correct answer for this 4.4 you might think sir what if it was something else okay let's say it was 4.4 71 and I want to get rid of these two numbers I want to get rid of these two numbers no worries compare it with the number 50 you can see it is more than 50 the number 71 is more than 50 so what you will do is when you are rounding it off you will add one to the previous digit and this will become then 4.5 because 471 you can see is close to 4 .50 500 is close to 471 so I did not want this so it is basically going to be 4.5 got it similarly imagine if it was 4.45 sorry 4.45 and now I want to get rid of these two digits okay compare it it is exactly equal to 50 oh if it is exactly equal to 50 then the previous digit check is it even previous digit check is it even yes if it is even then keep it as it is if it is even if it is even then just keep it as it is guys it will be 4.4 only but just for the sake of discussion let's say it was 4.75 and I wanted to get rid of this two digits you can see it is equal to 50 check the previous digit oh what is the previous digit digit it is odd number it is odd number if it is odd number add one to it so what will it become it will become eight so the final answer will be 4.8 after you round it off that is how you solve the rounding of of digits got it everyone how to solve these questions very very important discussions I hope you are remembering everything now I hope you remembering everything okay for 4.35 if you get rid of 5 check the previous digit three three is odd so what will you round it up to four 3 + 1 is 4 cool understood all right perfect let's go to the next question coming up on your screen what is it a physical quantity is described by the relationship this particular thing if the relative error in a BC are 2.13 and0 five what is the relative error in P guys this is directly based on that power formula which I just G you write it down in proper Powers already done okay so the relative error in P will be relative error in a what is the power of a it is half plus relative error in B what is the power it is basically two plus relative error in C what is the power it is three plus power of D is four ignore the negative sign so into D's relative error so that's it so so relative error in a is 2% two * relative error in B is. 1% relative error in C is 3% plus d error is point how much 5% do the math and tell me quickly how much is it this is. 1% plus 2% plus 9% plus 4 into .5 that is 2% everybody what is the answer that you are putting is it C Paka for sure yes .1 +.9 1 2 + 1 3 3 point yes 3.2% perfect this should be correct answer very good so now you have got a complete hold of this chapter I believe if you got that confidence I hope you have smashed the like button I hope you have hit the Subscribe button and by the way let me also remind you that the J Test Series right now is live for the last minute preparation I had made a video of this I don't know how many of you have seen it it's just for 399 rupees do not forget to check it out I have given the complete details over here it's also there in the link of the description box Last Mile test series click on this particular link it will give you the last mile test series guys $4.99 for 10 tests and 150 books access digital copies if you are okay with only five tests then that is there for $3.99 these are all all India level mock test series with solutioning as well as ranking this is what you will need after this class so make sure you are participating in these test Series this is irrespective of whether you already have a test Series in your coaching this is all India level level okay keep that in mind all right let's start let's start with the next concept what do we have the next concept projectile motion and yes all their parameters related to the projectile motion okay uh do you have to byal important Dimensions no you don't have to don't sit and waste your time for example they ask you this kind of question what is the dimensional formula for example Mutual inductance what is the dimensional formula for Mutual inductance will you sit and byart it no how many things will you by heart just think of a formula related to Mutual inductance and self inductance so mutual inductance will be two is dimensionless dimension of energy dimension of energy divided by dimension of the current dimension of the current whole Square so this will be the easier way to tackle such a problem remember a formula I mean formulas anyways you remember so that's how you do this got it all right perfect okay moving on now to the projectile motion Concepts and the formulas let's revise it quickly a projectile motion is a motion where you throw a body only under the influence of gravity and acceleration due to gravity always acts down and it is not partial towards the masses meaning even if it is a heavy object or a light object acceleration is the same irrespective of the masses and it is approximately 9.8 but if you you want to make it more approximate it is 10 m/s Square for easy calculation purposes now every time acceleration acts down it is never horizontal so whenever you throw an object at an angle or vertical or throw it from a hill doesn't matter how it is going whether it is going a curved path whether it is going up and down whether it is just coming from the top to bottom always the acceleration is downwards acceleration in x-axis is zero this also is very important because because if there is no acceleration in the horizontal Direction no acceleration no change in velocity so in the horizontal motion velocity will not change it's only the Y component the vertical component whose velocity will continuously change so horizontal component will never ever change is this absolutely clear my dear Warriors yep okay so x velocity is usually U cos Theta because if this is U and this is the angle obviously the horizontal component will be U cos Theta and the vertical component will be basically U sin of theta this component will definitely change this component will definitely change this component will obviously be a constant that is what it is next important thing the time of flight maximum height range trajectory velocity at any point angle at any point all these uh formulas let's revise them if you want to find the total time of FL the formula is 2 U sin Theta by G if you make it vertical if it goes just up and down sin Theta will not come because Theta will be 90 Theta will be 90° sin 90 is 1 so it will become 2 U by G for vertical motion for projectile motion it will be 2 U sin Theta by G U is speed G is acceleration Theta is the angle of projection remember this number two also plays a role see if it is just going up it is U sin Theta G if it is just coming from top to bottom it is again U sin Theta by G so time taken to go up and time taken to come down is equal and it is U sin Theta by G so time taken to go up and come back is that's why two times U sin Theta by G is that okay everyone clear awesome next maximum height reach so when you throw a projectile like this what's the maximum height that it reaches from the ground level that formula is u s sin sare Theta / 2G again remember the 2 is below over here that's something which many students Miss usually in the height formula range it is U Square s not Square this is 2 Theta or 2 sin Theta cos Theta sin 2 Theta remember is 2 sin Theta cos Theta that is your trigonometric expansion divided by G there is a special case in this for maximum range like if you throw it like this or at a different angle you know the ranges could be obviously different so the range is maximum as you can see when you throw it at 45° so that's when the range is maximum also notice one more thing the ranges are equal for compliment angles only for 45° there is no complimentary I mean it is itself so for 30° and 60° the range is going to be the same 20° and 70° range is going to be the same 10° and 80° range will be the same so complementary angles the range will be equal next the path of the trajectory meaning as this projectile motion continues if you take any point it will have some y-coordinate it will definitely have some x coordinate the coordinates are related with this equation x tan Theta minus half GX s by 2 uh sorry U sare cos Square Theta and as you can see it is a quadratic equation if it is quadratic that means this Gra graph will be a parabola it is going to be a parabola so the motion is not just any random curve like hyperbola or ellipse it is a parabola it is going to be a parabola very good similarly if you take the velocity at any point then you will notice the velocity at any point will have two components X component and the Y component so X component will always be constant y component you can use kinematic equation to find it out the angle of that velocity yes the velocity will be making some angle this will be v y this will be VX this will be Theta for example or let's say five so that will be VY by VX which will be tan five remember the angle will keep on changing as it moves okay the angle will keep on changing correct all right all right perfect moving on to some questions ready for some questions get ready for it I want want everybody to answer it in the chat box the initial speed is U the highest point during the motion the speed is root3 U by two what is the time of flight now if you recollect the formula for time of flight it is nothing but 2 U sin Theta by G the problem is G is given U is given sin Theta is not known because Theta is not given don't worries hint is given here in that particular projectile motion it is mentioned that initially the speed was U Theta not known but at the highest point the velocity is given to be < tk3 * U by 2 at the highest point what is so special at the highest point this velocity is the horizontal velocity only because the vertical velocity becomes zero the net velocity is just horizontal so this is just ux and what is is ux going to be what is ux going to be it is just going to be U cos Theta therefore COS of theta will be < tk3 by2 therefore Theta who cause is root3 by2 30° oh so Theta is 30° so I'll just put 30° over here and then solve for the problem so 2 U sin 30° / G so s of 30 is basically half so half into 2 is canceling out so it will be just U by G so which is B option is this clear my dear students everybody with me shall we proceed ahead to the next question awesome moving on to the next question guys don't spam yeah spam the answer but don't spam and disrespect anyone or else the admin will come and I I know that the admin will block or probably you know time you out so don't spam or disrespect each other but answer spam BB BBB a a cccc DD DD whatever it is Spam it I want everybody spam as answers doubts spam it no problem sir you are loving I'm loving the class spam it no issues no issues with that equation of project tril is < t3x minus half GX s the angle of projection is how much interesting now compare it with our standard formula comparing it Y is x * of tan Theta minus half g x Square by u² cos² Theta if you just compare quickly you will see that tan Theta is < tk3 so therefore tan Theta is otk of 3 and here G by 2 is there G by 2 is there therefore u² cos Square Theta is 1 x square is there G is there 2 is there so u s cos sare Theta is going to be 1 perfect everyone with this okay okay but we want Theta that's it so tan Theta is root3 therefore Theta is nothing but 60° so Theta is 60° that means B option should be correct very good if the question was what is the speed then substitute it back over here so therefore u² cos Square 60 will be 1 therefore U sare cos 60 is half so it will be half square is 1 therefore U sare will be 2 square therefore U will be 2 m/s so if the speed was asked this is how you can do it Theta is asked this is how you can do it time of flight is asked you know the speed you know the Theta use the time formula maximum height is asked you know U you know Theta find the maximum height using maximum height formula range is asked U is known Theta is known use the range formula that's how you can solve anything and everything if you know the equation of trajectory got it just compare it with the standard formula you will get most of the things just compare it next particle is thrown with an angle of 60° with a speed after some time the direction of the Velocity is 30° above the horizontal the speed of the particle at that moment when it is making 30° how much that is the question let's see how many of you can do this come on my dear students very good very good many people very good Vijay nanja and Tamil Arjun awesome aswin very nice to see all your answers Sanjay very good very good Nilan Kevin Joy awesome ratan Narin Girish PMA broken heart is flirting over here sir do you think it'll be easy for 202nd gen no point thinking about or stressing about it I'm telling you it will be the most difficult paper what will you do if I tell it is very easy paper what will you do I mean think it is going to be the most difficult paper and go what is the worst thing that can happen most difficult paper though that's it go with it okay it will be difficult for everyone number two if it is very easy then understand if you don't complete the paper on time and if you don't solve enough number of questions that is a big disadvantage so don't think if it is easy paper it is good if it is very easy paper everybody will do well and if you are not well then that's it your percentiles will decrease remember your scores are compared with the people in the same shift so be careful about it yeah so let's see what is the answer for this guys by the way as this projectile motion goes like this and initially what was it 10 m/s 60° so this was 10 and this was 60° and somewhere over here I don't know what the speed is but it is definitely given it is 30° what is say is that whatever this velocity VX will be that will be the same velocity ux yes both these velocities will be equal because acceleration in the X direction is zero so velocity is going to be the same that's it what is this velocity going to be this will be 10 cos 60 cos 60 is basically half which means it is basically going to be five so this will be equal to what on this side it will be V cos 30 what is cos 30 < tk3 by 2 so what will be V it will be be 2 * of 5 and divided < tk3 therefore V will be 10 byun3 10 byun3 is there over here so option number D how many of you said it many of you said it some of said option A that is wrong be careful easy question easy question didn't understand what you're saying okay uh you can watch it as no problem for revision no issues next let's go to riverboard questions next let's go to riverboard questions all right okay perfect let's solve this oh by the way in these projectile motion questions sometimes you sometimes you know they will um ask you things like uh when is the velocity going to be making 30° or when is the velocity going to be making 40° 45 degrees and such sort of things so if such sort of question comes say they tell you you know I have thrown that thing with some angle and after some time it is already given that the angle made is so and so let's say it is given to be 45° so at what time will it happen so for example if the velocity is making 45° what does it mean the X and Y components the X and the Y components both are going to be equal because 45° means it is an isoceles right angle TR so VX will be equal to V so if VX is equal to VY if VX is equal to VY VX is always going to be ux VY will be uy + a y into T equation of kinematics here remember acceleration is not there in X Direction U is nothing but U cos Theta uy is nothing but U sin Theta so acceleration is netive G and this is time so from this you'll get U cos Theta minus sin Theta or basically put that GT term over here so GT will be U sin Theta minus U cos Theta so therefore time will be U sin Theta minus cos Theta whole thing divided by G so that's how you can find out this particular time okay Theta is basically this Theta is basically this U is that so you can find the time when the velocity makes certain angle such sort of questions can can come okay yes perfect let's go to Riverboat related questions and formulas now remember over here usually you'll be given two Banks okay and the river will have some speed the swimmer or the boat will have some velocity so U is velocity of that boat in Still Water meaning if the water moves this velocity will get get added if the water is still in that still water the boat or the swimmer can swim at certain speed so the river will have certain speed let's say that is W so w becomes the velocity of that particular River so then you get V which is the net velocity of that particular boat or swimmer with respect to the ground means the bank with respect to the bank or the ground so that will be basically this and therefore V bar will be the vector addition of U Bar and W bar U Bar and W bar keep this in mind everyone okay till this point clear next important thing this will be the distance between the banks of the river and they might ask you what is the time taken to cross what is the time taken to cross always whenever you have to find the time taken to Cross C to cross the river you have to go from One bank to other bank the other bank is on the vertical side the upper side y side so you just consider vertical motion or perpendicular to the bank motion so time is Distance by speed so Distance by the speed everything along the crossing Direction what is the distance distance is D what is the velocity along that cross the velocity along that cross if this is the velocity just consider the Y component don't consider the X component or even the total velocity no only consider the Y component that's it that is the time taken to cross is this clear everyone next as you proceed as you proceed you will see that you will reach somewhere over here on the other side of the bank so yes there is some drift which will occur there is some drift which will occur this particular drift will be the time that you spend in Crossing distance is time into speed so basically the speed along the river the speed along the river so time taken to cross time taken to cross is just over here we just figured it out whatever it was same thing okay the same thing speed along the river is basically VX so this multiplied by VX is basically going to be the drift this is going to be the drift got it no other formula will be needed now there are two special cases in this what are those two special cases first is you want to cross it in the shortest time if you want to cross it in the shortest time and the second one is basically the shortest distance you don't want to cover extra distance so say for example this is the banks of that particular River you want to cross it in the shortest time means you will push yourself or Swim along the perpendicular Direction yes the river will pull you this way and your resultant will be like this and you will end up drifting somewhere over over here okay you will definitely encounter some drift okay because of this here if you notice the time taken to cross which will definitely be the least will be distance between the banks whatever it is let's say d it will be D divided by that vertical speed vertical component will be just going to be U so it will be just U over here that's it that's what you will put so this is V this U is also going to be VY U is also going to be the vertical component so that is the minimum time taken to cross the river whereas over here in order to ensure that you have minimum drift so this is the river velocity your resultant velocity will be perpendicular so therefore you will swim against the current like this this is how your U will be this is what your V will be and maybe this is that particular angle and you will have no drift in this this case so there will be no drift in this particular case got it so this is how you'll be swimming for shortest distance you can measure that angle it is not that big a deal so sin Theta or cos Theta you can find out because sin Theta will be nothing but nothing but what is it sin Theta will be nothing but opposite by hypotenuse so w by U so that's how you can find the angle at which you should swim so that your resultant is perpendicular and you encounter no drift here U is perpendicular here V is perpendicular that's the difference cool all right let's solve some questions here it comes on your screen come on uh har Naran I'm telling you we are trying to cover the entire things as much as possible all right all high weightage topics concept question concept question concept question all right so 11th and 12th standard entire syllabus this session might go on four five 6 hours who knows the boat crosses a river of width 1 kilomet shortest path is 15 minutes if the speed is 5 then what is the speed of the river come on think about it okay the boat crosses 1 kilm width of river shortest path in 15 minutes the speed of the boat is five then what is the speed okay of the river so as you can see certain data points are given to me the width is already given it is nothing but 1 kilomet okay now uh in 15 minutes okay so my resultant velocity will be like this the river velocity will be like this okay and still water this speed is also given to me how much is it it is going given to be five okay now if this is the scenario think about it the time taken to cross the particular River will be Distance by the vertical component the vertical component in this case is itself V distance of that river banks is 1 kilomet time taken to cross is 15 minutes 15 minutes in hours is 1 14 of an hour remember 15 minutes is basically 1x4 of hours this was 1 kilometer this velocity will be kilometer per hour everything is in kilomet per hour so velocity will be 4 kilomet per hour okay so I got this value of velocity as four obviously this is going to be a right angle triangle if this is five this is four this is a Pythagorean triplet guys 4 five and this will be three 4 53 37 53 90 triangle so answer should be three that's it very very easy got it awesome awesome very nice D very good shasa Padu only J awesome Tamil moving on to the next question river is so much meter wide river speed is given boat starts perpendicular how far from the point directly opposite does the boat reach meaning the drift is asked drift is asked this is One Bank this is another bank the boat guy is trying to swim like this with what velocity this is basically five okay the river speed is how much reverse speed is uh 3 m/ second so the resultant velocity will be like this and you will end up reaching here you intended to reach over here so obviously there will be some drift over here and that drift will be asked now the drift is what is the velocity along the river what is the velocity along the river into the time taken to cross if you notice the velocity along the river is exactly three the velocity along the river is exactly three I just don't know the time how can I find the time to cross the time to cross is d by v y distance of that river is 20 M vertical speed is just five which means it will be 4 seconds just put that four over here 3 4 are 12 so 12 m should be the answer correct it is 12 M got it everyone no it is not 15 it is 12 very good abishek disaster awesome okay lunch break after some time we'll have the lunch break don't worry yeah cool shall we go ahead ready for the next question guys okay here we go the boat is moving with a velocity of 3 I plus 4G velocity is - 3 i - 4G with respect to the ground the relative velocity of boat with respect to the water okay let's see what an all is given to me the boat is moving with the velocity with respect to the ground meaning this is the net velocity so V is 3 I + 4 JC the river water is moving with this much velocity that means water velocity is - 3 i - 4G remember this is always the resultant of this Plus u u is question mark U is basically question mark and we know U plus W gives me V therefore U will be V minus W so what is v v is basically 3 I + 4 J this whole thing minus minus what do we have over here minus water velocity which is - 3 i - 4 G okay so what will I eventually get minus - is plus 3 I + 3 I 6 I um-- plus 4 + 4 is 8 6 I + 8 G so 6 I Plus 8 J cap which is option number c so you need to know this equation without that you will not be able to do this question if you know each term separately what it means and you are consistently using same formula same symbols same alphabets it will get stuck in your head or else once you're reading from one book once you're reading from another note once you're making some other manner of remembering it it will become difficult okay awesome awesome great moving on broken heart your Priyanka is not here I think Priyanka is studying for J if you want to meet Priyanka you'll have to visit inside the it campus yeah because you know she's studying properly so Priyanka will go into the I campus but oops so sorry you will not be allowed inside the it campus because you're not studying no so the gatekeeper only will be like stop where is your ID card and you'll be like oops I can't enter inside I so you will not be able to meet Priyanka so don't waste your time but if you want to meet Priyanka you better study then maybe maybe there is a chance all right cool moving on to the next question coming up on your screen yes oh it's a concept and we are going to Newton's Laws pulley Concepts and uh yeah Newton's Laws all right now whenever you have a pulley pulley just changes the direction of the the String's tension and if it is a fixed pulley like the one over here okay the force required to lift the load is equal to the weight of the load so meaning if the pulley is over here and you have some string wrapped around it and there is a mass over here the force which you require will be exactly equal to the weight of that mass that's all okay Force required will be exactly equal to the weight of that mass the pulley is stationary mass is stationary nothing is moving acceleration is zero it's a fixed P nothing is moving acceleration is zero but the moment things are moving and all of that then things will change you have to use Newton's law also remember one more thing also remember one more thing that sometimes the pulley will be here the pulley itself might have some mass and then maybe the string wrapped around it will have some tension it will have some tension the pulley itself might have some Mass which is mg so the roof on the top might exert some normal reaction the roof might pull it up and how much force will it have to apply mg is there and this tension and this tension so 2T so the roof will apply a force of mg + 2T that is what you need to keep in mind if such a question comes also so whenever you draw a block which is connected to a string and maybe it is accelerating up or down then that block will experience a tension because of the string it will have its own weight mg when you write Newton's law which is net force is mass into acceleration always the direction of the acceleration is considered as positive so it will be tension minus mg is equal to M * of a tension minus mg will be M * of a okay keep this in mind if it was accelerating down then it will be mg minus t this will be positive so mg minus t will be Mass into acceleration that is something again you need to keep in mind now standard formulas now there are many standard formulas instead I will tell you an easy way to do any question within seconds this is strer strick look at what strer strick is observe carefully if you have a pulley you have a mass and you have another Mass over here and you have to find what the acceleration is always remember the trick is acceleration is the pull Force minus the opposing Force okay the whole thing divided by the mass which is moving all the masses which are moving the total mass which is there so if you apply that concept over here this acceleration will be the pulling Force the pulling force will be nothing but m2g so m2g opposing Force it's trying to go up this m1g is opposing it so it will be minus m1g upon the total mass which is nothing but M1 + M2 that's it so it will be nothing but M2 minus M1 divided M1 + M2 into G if you draw the free body diagram and then try to solve it for the tension right if you solve it then the tension will come out to be 2 M1 M2 divid M1 + M2 into G that's a standard formula remember it similarly let's say I apply the same thing to another question let's say there is a mass here there is a pulley here like this okay and there is another Mass here this is let's say M1 let's say this is M2 now this is coming down so the pulling force is m1g let's say maybe there is friction over here so the opposing force will be mu m2g mu m2g so if you want to find the acceleration the pulling force will be m1g opposing force will be mu m2g whole thing divided by the total mass which means M1 + M2 that's it that is the answer okay now there is a trick in this also where imagine you have a pulley like this this is mass one let's say this is mass number two let's say this has mass pulley itself has mass then how do you find the acceleration well first of all the pulling force will be m2g opposing force will be m1g so numerator will not change pull minus the opposition total mass M1 and M2 are there M1 + M2 but what about this Mass pulley itself has mass so this is a pulley with mass this is nothing but pulley with your mass what do you do in that case in that case what you do is basically take the equivalent of the pulley let's say the pulley is given to be a dis let's say it is given to be a dis remember the formula for moment of inertia for a disk the formula is M3 r² M3 r² by 2 so this number 1 by two is very important that number factor will come over here the equivalent mass will be M3 by 2 that M3 by2 will come over here that formula which is there in moment of that number which will come 1X 2 1X 12 1X 4 1X 3 2x 5 2x3 that factor will come over here that will be basically the equivalent mass of rotation that is the trick I'll give you one more question don't worry from that you will be absolutely clear let's say this is mass one okay this is another pulley just like the previous question this is Mass to this is mass 3 and let's say it is a solid sphere this is nothing but a solid sphere okay and this is coming down with some acceleration this acceleration assume that this is smooth for now assume this is smooth for now pull Force how much is the pull Force m2g opposing force not there only so minus 0 total mass M1 is there M2 is there plus solid sphere what is the moment of inertia formula 2x 5 M r² so this number will be 2x3 * of M3 so very easy to solve these questions if you don't know moment of inertia then please beart all the moment of inertias of all the things five six things only are there just byart it it will become very very easy is this clear everyone yes isn't it l by R to cancel the radius yeah you can do that it is a more complex way I'm telling you very easy way just remember the factor which comes what is that factor 2x 5 2x 3 1X 12 1X 2 1 just do that it will become very easy so even if you have a more complex question something like this let's say there is a mass here okay and there is a mass here let's say there is 2 m Mass here this is let say a dis and then you know it goes to another pulley over here let's say this is a the solid sphere let's say this mass is 5m and this is going on a inclined plane like this okay this is let's say 4M and this inclination let's say is uh 30° like that and you know it's known to me that it is let's say for example assume to be accelerating like that so how do you solve this problem it's a smooth plane again acceleration is the pulling Force pulling force will be along this direction remember mg will have two components mg 4 mg will have two components one here one here this will be not pulling it this will be pulling it so this will be 4 mg s30 correct so it will be 4 mg sin30 opposing force will be here only so it will be just mg so minus mg over here the whole thing divided by the total mass m is is there 4 m is there m + 4M plus this is a disk for a dis what is the formula guys M R square m is 2 m r² by 2 so the equivalent mass will be how much equivalent mass will be how much 2 m by two which is just m is that right so the equivalent equivalent mass in this case is how much M only because 2 two got cancel for a solid sphere what's the formula 2x 5 mass mass is 5 m r² so so 55 cancels equivalent mass will be how much 2 m so just put 2 m over here that's it that will be the acceleration isn't it a simple method guys everyone let me know understood how to solve these questions okay all right this was sign I missed that sign over here sin 30 yeah if you want to solve it you can solve it it is not that difficult so the acceleration will be sin 30 is half 4 into half is 2 so 2 mg minus mg the whole thing divided by 1 + 4 5 5 + 1 6 6 + 2 8 so 8 m so 2 mgus mg is mg so mg by 8 m so mm cancels it will be G by 8 so G by 8 will be the answer for this okay cool clear understood very very simple let's see if you can solve this now find the acceleration and the tension okay numerical type of question numerical type of question all right how to get the well pulling force is only over here there is no friction all surfaces are smooth okay perfect so acceleration will be pulling Force which will be just 4G 4G there is no friction only so it is completely smooth no Force at all minus 0 upon total mass which is 4 + 2 so it will be 4 G by 6 or if you want you can write 4 into 10 divided 6 4 goes 2 * 6 goes three times okay so it will be basically 20 by 3 m/s Square this is done now you draw the remaining forces all right and you can just say this is basically tension so for this Mass tension is mass into acceleration but acceleration we just figured it out to be 20 by3 so it will be 40 by3 Newton so tension is 40 by3 Newton no other force is there in the horizontal Direction vertically yes there are forces but that is not what is important tension is mass into acceleration job done and tested okay so yes 40 by3 Newton and 20 by3 m/s squ uh yeah I'll be uploading the session PDF in the description box of this particular video only not the Jungle Book or anywhere else okay uh and I'll tell you one more thing PDF is very important but you have to also attend the class if you just see the PDF it'll be like okay okay okay but if you just see the class also it'll be like ha haa so PDF is important because after the class you will go through the problems you'll go through the concepts session is important because you'll understand you will develop that aptitude you will be motivated you will be getting the proper explanation so both the things will be important and you have to get the PDF after the class is over okay you will get it don't worry moving on system shown in the figure the acceleration of 1 kg mass and the tension in the string connecting between A and B is how much okay so both these masses I think we can just couple them together that will be be easier right yes so I can just couple them together that's one single mass of how much 3 + 1 is how much it's just going to be 4 kg yes it's just going to be 4 kg so the 4G force will be over here and 3G force will be here this entire system will accelerate like this this will obviously go up because this is lighter this is heavier so the acceleration will be pulling Force which is 4G opposite Force which is 3 G upon total mass which is 4 kg + 3 Kg 4 + 3 so 4 - 3 is 1 so G by 7 so acceleration is G by 7 and uh the find the acceleration of 1 kg Mass 1 kg mass is going down so G by 7 will be downwards G by 7 downwards yes definitely it is here now the question is also about the tension connecting them so draw the free body diagram of that 1 kg Mass you will notice well 1G is here there is some tension between the ropes which we have to find and it is going down with G by 7 so the force equation will be 1 g - 3 is equal to mass into acceleration so tension will be 1 Gus G by 7 1 - 1 by 7 is going to be 6 G by 7 so tension is 6G by 7 which is exactly mentioned over here so C is the correct answer perfect cool yes C for captus awesomeness awesomeness moving on to the next concept of frictional force well standard things friction is of two kinds static and kinetic when you try to push something first the static friction will come into play and it will try to oppose whatever Force you are applying if you apply 2 Newton Force then it will also apply 2 Newton in the opposite direction if you apply three it will apply three 4 4 5 five like that let's say till 9 Newton till 9 Newton you applied 9 Newton Force you can bear it but if you apply one 9.5 Newton Force you immediately see that it starts moving which means the force of friction was not able to hold it in static nature so it has started sliding it now enters a different kind of friction called as the kinetic friction and the kinetic friction is always less than the threshold friction the maximum frictional force because once a body is moving the friction experienced is less because the surfaces you know they will just fly on top of each other not literally because there will not be enough time for the you know uh surfaces to interact with each other to get trapped or to get stuck so that's the reason why when it is stuck it is difficult to move but once it is moving it is easier to keep it moving so so you will see that the kinetic friction is usually going to be less static friction will be less than or equal to MSN this MN is basically the maximum frictional force mu is the coefficient of static friction n is the normal force on that particular surface okay normal force on that particular surface kinetic friction is obviously less than your FS Max and it will be mu K into when mu K is the coefficient of kinetic friction as you can see in this particular graph as you can see in this particular graph mu K will definitely be less than mu but they're not very different small difference will be there but usually mu is smaller than Ms okay then also remember angle of repose it's a very important concept where that is the angle that is the angle after which any box or any body which is kept it begins to slide it just it just begins to slide so you can keep increasing the angle at one angle it will start sliding so that angle is Alpha angle of repose tan of angle of repose is coefficient of static friction coefficient of static friction yes you'll be having similar session for chemistry and Mathematics too limiting static friction is also FS Max yes FS Max is the same as limit limiting friction limit of that friction limiting friction static friction threshold friction everything means the same thing don't get confused okay FS Max all these are same same same things very good guys now if if uh the uh remember if basically the inclination is less than the angle of repose it will not slide if it is more then it will slide down with some acceleration so if tan Theta is more than mu remember tan Alpha is equal to Mu it is just on the verge of sliding but if Theta is basically more than Alpha definitely it will start sliding and the acceleration while sliding is G remember this value G common sin Theta minus mu cos Theta if friction is absent mu will be zero and the acceleration for a smooth surface will be G sin Theta if it is having friction G sin Theta minus G mu cos Theta or G can be taken common very important acceleration formula keep this in mind is that okay another important thing related to friction many times they ask you this question if you have a circular track and a vehicle is going on that circular track how much can be the maximum speed without it skidding off the surface that maximum speed on that curved track horizontal is root mu RG mu is coefficient of static friction G is acceleration due to gravity R is the radius of that track that circular track which is there the radius of it so this is the maximum speed formula these are the critical things which you should remember also in the angle of repose they can ask you these kind of questions where they will give you a heap of sand and if you keep on adding sand I mean it will keep on becoming like this but after a point it will not increase in height rather it will just become a cone if you add more sand it will just you know it will just slide down like this and you know it will have a constant angle this angle is also the angle of repose because if any more sand is added it will just slide down because the inclination angle will be more than Alpha there so if you add more sand it will just slide down over here and it will ensure the angle of inclination of that heap of sand is basically Alpha this concept is also used in that insect in the bowl question so you will have a bowl like this you will have a bowl like this and there is an insect and it can only climb till certain height why because as you move up the inclination will increase and there is a certain instant when that inclination will be exactly Alpha so the insect inside can only reach till here from the bottom point so this is basically the maximum height which the insect can go this is the maximum height which the inser can go when the tangent drawn makes an angle of alpha which is the angle of repose these questions are standard questions all right Perfecto let's do some questions on this and then we can have a small break definitely okay how to find the friction Direction in circular motion for different cases okay I'll tell you something always remember one thing static friction always opposes the tendency the tendency of motion whereas kinetic kinetic friction always opposes the actual relative motion that's how you do it so say for example you have a curved track and let's say there is a vehicle which is going like this okay vehicle which is going like this what is the friction which will be acting first of all it will be static what is the tendency of the vehicle always static friction opposes the tendency remember the tendency of the vehicle it tends to fly out it tends to fly out hence the static friction will pull it toward WS inside hence the static friction will pull it towards inside then there is one more question where there is a circular drum and that circular drum like a washing machine is spinning the axis is vertical imagine the clothes or the objects inside are spinning like this and they all stick to the circular wall or the curved wall of that cylindrical drum so imagine such a scenario guys this is that circular drum it is spinning like this then obviously it wants to fly out any object over there any object let's say over here okay I'll just take it over here this is our object it will try to fly out it will try to fly out that's why there will be a normal force on it from the wall of the container from the wall of that cylindrical container it will tend to fly out so there will be centri Fugal Force outside centrifugal force out side because of its own weight it will try to fall down because of its own weight it will try to definitely fall down the weight of it now because it wants to slip down friction will prevent it from slipping so static friction will act upwards so static friction will act upwards then got it understood very good similarly imagine that you have an inclined plane and let's say you have have kept a box on it and somebody decides to push to push this particular box like this with a force more than mg sin Theta with a force more than mg sin Theta remember mg sin Theta will act downwards and somebody is pushing it with more Force than mg sin Theta so what will happen it will have a tendency to fly up it will have a tendency to slide tendency to slide up the incline plane so what will static friction do static friction will oppose it so static friction will act like this got it now how to find the direction of the friction in any given scenario all right kinetic friction is always easy because you can already see the motion happening so say for example you know you have one surface like this this is going with 7 m/ second and let's say this bottom surface is like this which is going with 9 m/s then you sit on this and look at this so sit on the bottom guy and then look at the top block you are moving fast this guy is moving slow so this guy will appear to move relative motion of 2 m/ second so what does kinetic friction do it always opposes relative motion so the friction on this guy will be like this got it so always check the relative velocity and then solve the question for kinetic friction awesomeness moving on now there is a mass which on a rough contact with a plane inclined at 30 find the coefficient of friction if it is just I think on the verge of sliding and all that it is just about to slip just about to slip means the concept of angle of repose should be used so tan of alpha should be mu s so static friction is what is asked angle is is already given to be 30° so 1 by < tk3 is Mu s so 1 byun3 is a standard value 57 because root3 is 1. 732 so it will be. 57 I think around that much yes it is 57 that's 1 byun3 okay so that's how you solve this particular question usually it can be asked as an integer type so you might have to go till the second decimal better to remember these root 1 by root values and all of that if a body takes time T to reach the bottom with the horizontal angle of inclination Theta if the plane is made rough then it takes double the time what is the coefficient of friction okay let's do this if the plane is smooth if you release that block it will reach over here in time T the distance covered is X it starts from rest and the acceleration for a smooth surface remember will be G sin Theta so use kinematic equations s equal to U + half G sin Theta into t² okay in the second scenario in the second scenario the same surface is now made to be rough the same block is left from rest and it reaches over here covering a distance of X only but in double the time but this time the acceleration will be g into sin of theta minus mu cos Theta that is the formula remember I just gave it to you okay so again use chematic equations so s = u + half into G sin Theta - mu cos Theta but the time taken is 2T so 2T whole squ all right X will be equal question is find the coefficient of friction Theta terms okay so X is going to be the same so take this X from here so it will be half G sin Theta into t² okay is going to be equal to I have half over here G over here where very good sin Theta over here minus mu cos Theta over here and this 2 T sare will become 4 t sare t sare t Square cancels half half cancels GG cancels so what am I left with on the left hand side just sin Theta is equal to and uh over here is that right G got out 2 got out T sare also got out sin Theta is remaining okay so sin Theta * 4 that is 4 sin Theta minus mu into 4 into cos Theta that's what it is so take that uh 4 mu cos Theta on this side 4 mu cos Theta on this side is equal to 4 sin Theta over here minus that sin Theta minus that sin Theta 4 - 1 is 3 so 3 sin Theta is equal to 4 mu cos Theta so okay okay mu will be equal to 3x 4 sin Theta by cos Theta which is 3x 4 tan of theta so 3x 4 tan of theta which is a option that's how you do it is that okay cool perfect awesome option A is the correct answer very good guys very good awesome awesomeness moving on to the next question yes this is also a very popular question if there is a block which is sliding with a force f at an angle coefficient of friction is Mu the acceleration a is given by very nice question reason why it is nice is because Normal will not be mg yes see the weight of the block definitely will be mg but this normal over here won't be mg because this force will have two components one over here one over here this will be F cos Theta this will be F sin Theta and apart from that there will be a normal reaction now the total acceleration is towards the right side and we have to find that out and uh well I think friction is also going to be there because it is going towards the right side so friction is also there that is Mu into n mu into n so I think we need to find the normal first so if you do everything in the y direction the normal plus F sin Theta will be balanced by weight therefore F sorry therefore normal will be mg minus F sin Theta okay perfect now let's do everything in the horizontal Direction in the direction of acceleration everything is positive so therefore F cos Theta minus the friction which is Mu into n will be equal to mass into acceleration okay so F cos Theta as it is Mu K as it is normal I will just get it from here which is mgus f sin Theta is that right is equal to mass into acceleration rearrange this I think and put Mass below so F by m cos Theta minus mu k g m m gets cancelled minus minus becomes plus so mu k f sin Theta / m is equal to a therefore acceleration will be take f by m common cos Theta no plus cos theta plus uh mu K sin Theta and minus mu K into G that is what it should be yes that is what it should be yeah it's the same thing however you want to write it f by m cos Theta is there yes minus mu kg is there minus minus becomes plus mu k f by m sin Theta is also there yes this is the correct answer yeah it is C option just check this out okay the options look very similar to each other so you need to be very very careful you need to be very very careful Harish I don't know the way it is going I think it might go on like that only all right kinetic energy of a particle is changed by 300% find the percentage increase in its momentum did we miss a slide oh yeah we missed a slide kinetic energy yeah okay we'll come to this after a short break just give me some time just 5 10 minutes and then we'll be back 10 minutes break and then we'll continue e e e e e e e e e e e e e e e e e e e e e e e e hello hello all right the time is up uh get all your friends back to the session because yes yes sir is here on Macar sankranti on bngal on Lori for your Festival celebration and in fact we are celebrating this Festival because we are J students by attending a class by revising the entire chapters revising the entire subject in fact in this one short Marathon for 99 percentile if you are a zero if you feel that you are not better than most other students if you feel hopeless if you feel demotivated this session is for you this will 100% boost your score just give me one day and that is today tomorrow there will be chemistry and then maths so these three days guys this is going to boost your scores like anything build your confidence so get all your friends because we don't want any student to be left behind neither should you don't think sir if I tell my friend to attend he will score better my rank will go down if that is the way you are going to think definitely your rank will also not go up so encourage everyone to attend this class because this is specially for all the kids and this is yes in English because many lectures are there in Hindi and many students don't understand it that well or don't connect with it that well so this is for all the kids who prefer learning in English and this is the number one J English Channel all right so let's begin uh no this is not thermodynamics uh welcome welcome hi Arya hi anshu hi Aditi uh 40 45 what uh welcome welcome welcome disaster welcome everyone uh no we are not not concentrating on J advaned in this particular session this is for January attempt J means 2025 okay so break is over the next concept one second let me just change the AC temperature H I'm already sweating all right h that let me get my pen okay work kinetic energy theorem states that the work done by all the forces externally and internally together that is the total work done changes the kinetic energy of the system where the ktic Energy Formula is half M v² or the square of the momentum by two times of the mass that's what work kinetic energy theorem is also when you want to calculate the work you have two options if the force is constant it is f do of s else it is integration of force with respect to the displacement this is when f is going to be constant this is when f is going to be a variable this integration also tells me that you can just take the graph of force with respect to displacement and let's say the graph is going like this you just measure the area under the graph this area whatever is there is the integration that area will give me the area will give me the integration of force with respect to displacement cool integration is area under the graph remember the areas which are on the top are positive area which is below is negative when you are doing the calculations all right so let's do some questions kinetic energy is changed by increased by 300 percent find the percentage increase in its momentum please do not use error formula because the percentages are very large in fact 300% so definitely you cannot use those error formulas yes break is over uh Niha and Akash yes the break was just now I think you just came after the break okay so uh welcome Anu all right maths and chemistry Aditi will be there tomorrow and day after one one day one one subject is going to be there is that right okay uh now here what we do is basically kinetic energy is changed by 300% let's say the initial kinetic energy was K then if you talk about the final kinetic energy it will be the old kinetic energy plus it is increased by 300% so 300% of K that is the change so which will be K plus 300% of K means how much 100% of kinetic energy means K 200 means 2K 300 means 3K so therefore this will be 3K so the final kinetic energy will be four * of K now our usual formula for kinetic energy and momentum is p² by 2m isn't that right so it also means that initial kinetic energy will be p² by 2m therefore the final kinetic energy this 4K will be also equal to the new momentum the new momentum Square by 2 * of M but wait a minute K is nothing but p² by 2 m so just put the value of K from here which was p² by 2m and this continues to be equal to the new momentum Square by 2 m 2 m 2m cancels so therefore that new momentum therefore that new momentum will will be 4 * of p² now take uh new momentum Square will be four * of P Square take square root on both sides the new momentum will be two times of that old momentum this can be also WR know as p + P which means it will be p + 1 p is nothing but 100% of P so this is basically the change of that momentum so the momentum incre Ines by how much 100% that should be the answer okay many people give a wrong answer I have seen many people giving 200% or even Sometimes some weird answers but that is not correct all right perfect thank you oh my god vn's Club you deserve a shout out it means a lot where can I go about it yep there we go oh my God thank you so much thank you so much for your Guru Daka I mean it was not really uh needed your like is also enough when you smash this like button and you subscribe to the channel that is really really grateful for me but thank you for the Super Chat sir you are the reason many students get into I nits and wishing happy Makar sankranti Pongal Lori to each and everyone thank you vn's Club means a lot let me just like this yes perfect thank you so much means a lot yeah vn's Club it I mean I don't know you are making me emotional by sending this because no teacher uh you know ever asks for such donations we tell okay please you know join our courses we just you know buy the material that we have worked hard on okay but this donation means a lot thank you so much thank you so much all right moving on to the next question coming up on your screen and uh let's see what it is okay there is a block which is kept this was asked in 2019 it is moving up with an acceleration of G by 2 the question is what is the work done by the normal reaction in time P what is the work done by it okay let's see how do we do this particular question first of all in order to find the work done what we need is the force into the displacement here which force are we talking about the question is the work done by normal so it will be the normal force it will be the normal force multiplied by the displacement of that particular body do I know the normal force not yet we can find it out well the weight of this box will act downwards the normal force will act upwards acceleration is upwards so normal minus mg is ma a therefore n will be mg+ ma a a is nothing but G by 2 so 1 + half is 3x2 so it will be 3x2 times of mg so that is our normal force so I'm just going to put that over here 3 mg / 2 still the displacement part is remaining how do I take care of it well I can use displacement is UT + half a t² initial velocity zero acceleration G by2 so put that over here into t² so it will be GT ² / 4 that's your displacement so put it over here GT s divided 4 that's it I think we can calculate the work now three m g into g g sare t² 2 4 are 8 so 3x 8 should be there somewhere yes 3x 8 is only over here so option D will be the correct answer perfect very good awesomeness very good clear close enough fourth option very good disaster yes shinan awesome all right puru thank you love you too B hopefully you are saying I love you to me only maybe not some other person over here because we have Sometimes some uh kids who are saying I love you and then I'm like thank you then the kid told me no sir it was not for you it was for that other person in that chat box I'm like oh sorry sorry to disturb you both continue all the best a particle of mass .1 kg subjected to a force which changes with distance as shown if it starts its Journey from rest and its velocity at 12 M will be how much okay so in order to do this particular question question find the speed force graph I think work power energy obviously because the area under this particular graph that area is going to give me the work and work area area is of a trapezium which is half into sum of the parallel sides multiplied by the height of the trapezium what is the parallel sides this is four units this is 12 units so the sum of the parallel sides will be 4 + 12 height of the trapezium is 10 units so this will be 4 + 12 16 16 by 2 8 8 into 10 is basically 80 so 80 Jew is the work done and We Know by work kinetic energy theorem work is final minus initial kinetic energy final kinetic energy is half into Mass which is1 into velocity squar it starts from rest it starts its Journey from rest so initially will be zero and the work done we just calculated it to be 80 Jew okay so now so now uh 2 into 0 ided 0.1 is v² therefore v² will be 80 into 2 160 divided .1 160 0 therefore velocity will be root of 1600 which is 40 so 40 m/s is option b yes that is the correct answer so that's how you use the concept of area under the graph to calculate the work you should know the standard areas of standard geometries like circles semicircles triangles squares trapeziums triangles all these things standard things and kinetic energy theorem which will give me change in the kinetic energy is the work done so I use that no need of kinematics no need of Newton's Laws as such all right yes some of them are pyq some of them are non pyqs okay both combinations are done home the I'm very good I'm scared please don't ask me such questions with such names I'm like are you going to rob me yeah home Thief right all right so what is the next question we have two masses connected with some spring and the question is if both of them are given the speed V then what's the maximum elongation what if they ask velocity in a and t graph if that is the thing chanya area under acceleration time is the change in the veloc vity so find the area of acceleration time that will be V final minus V initial if you know initial speed you can find the final spe okay CH all right uh home Thief no I have not forgotten you because I think first time a thief is visiting my class unless I forgotten this particular pseudo name okay so what is this this velocity is V this velocity is going to be V this is not stretch rest only initially then later on this mass will be here this mass will be here they both will be at rest there is some extension so I can say the kinetic energy of both the blocks goes into the spring potential energy eventually what's the kinetic energy half into M into v² two blocks so into two spring energy half K x² half half cancels so 2 * m v² is = K x² the question is elongation so x² will be 2 m by K into v² therefore X will be vunk 2 m / K velocity not given mass is it given 250 g 250 g is 1/4 of a kg spring constant 2 2 two cancels so it will be nothing but V root 1X 4 1X 4's root is nothing but 2 so V by two should be the answer which is option b yes that is the correct one B option correct Sia Prasad very good disaster thank you V Andes club and uh I'll always be the motivation for many many years to come that is the whole ambition of mine all right okay let's move on to the next one the next concept is of center of mass where you know you will be given standard geometries or some masses are placed here and there and you are asked where is the center of mass if there are Point masses then the formula is very simple you multiply each Mass with their coordinate multiply each Mass with their coordinate add them up in the numerator divide it with a total mass you will get the coordinate of the center of mass whether it is X Y or Zed now if you know standard geometries it will be very very helpful for you so let me put up some standard geometries right over here like for example if you take a triangle doesn't matter scaling triangle okay so the center of mass so the center of Mass is at the centroid Center of Mass is at the centroid and the formula for centroid is X1 + X2 + X3 whole thing divided by 3 comma y1 + Y2 + Y3 whole thing divided by 3 what is this X1 X2 X3 Etc these are the coordinates of these three points so it is always at the centroid this is a laminar sheet please understand that it is not a frame of wire it is a triangular sheet the center of mass is always at the centroid okay standard spheres um you know squares Etc it is always at the geometrical Center next thing obviously for for a solid cone for a solid cone the and the hollow cone Holo cone the formula is as follows for solid cone it is H by4 for Hol cone it is hge by3 from the base everything is from the circular from the circular base similarly you have a solid hemisphere half of a sphere because complete sphere I know it is at the center solid Hemisphere and then you have hollow hemisphere which looks like a bowl Hollow hemisphere empty bowl okay so the formula for Center of mass is as follows for solid it is 3 R by 8 and for hollow it is just R by2 this is also something which you should remember then you have this if you have an arc of a circle this is just an arc of the circle of a radius R the complete angle is let's say Theta then the center of mass will be let's say somewhere over here Center of mass will be somewhere over here so this distance this distance is given by R sin Theta by 2 the whole thing divided Theta by 2 that is the formula but instead of an arc let's say instead of an arc let's say it was a complete sector that means it is like a pizza piece it is like a piece of pizza like this over here then the formula is slightly different and the formula is slightly different but it looks very similar to this same thing R sin Theta by 2 by Theta by 2 just put 2x3 number over here just put that number 2x3 that's all then you'll get back the answer I hope this is absolutely absolutely clear everyone till this point awesome awesome great all right all right now next thing next thing whenever you have whenever you have two or more bodies making up another body like for example this some object is there let's say over here and another object is let's say over here and each of them have their Center of masses here each of them have their Center of masses here this is body number one this is body number two then together together what you get is a composite body together what you get is basically called as a composite that means it is made up of multiple body then the center of mass of that composite body is given by you take Mass one of the first body into coordinate of the first body and then you add it to the Mass mass of the other body into coordinate of it upon M1 + M2 that's it that is how you find the center of mass of a combined body but then the other way around is imagine you have a big body let's say the mass is M1 and from that you take out certain Mass from that you take out certain Mass let's say over here so this is the cavity which you create and that cavity's mass which was taken out is M2 so whatever is remaining is this shaded part so this is that shaded part so you have taken out something from another body so this is called as truncated bodies not composite truncated bodies the formula for Center of mass in such a case in such a case is given by here you will put M1 X1 as it is but instead of Plus you'll put minus M2 X2 and here also M1 minus M2 so that's the only difference in the formula is that okay everyone so the center of mass of the cavity could be here Center of mass of that whole big body could have been here Center of mass of that composite or that sorry the remaining body could be here that's how it goes understood Clearo all these formulas please remember it let's start with some questions oh uh uh this formula is also important where you shift things here and there so let me write it down over here so whenever it is given that the center of mass is not moving or it is found that it is at rest that is uh uh net external force is zero Center of mass is not moving then or basically velocity of center of mass is zero Center of Mass is at rest then you you can say that mass number one into displacement 1 plus mass number two into displacement two Mass 3 into displacement 3 that sum will always be zero M1 S1 plus M2 S2 Plus M3 S3 plus M4 S4 like that is zero what is this S1 S2 S3 Mass one moved here Mass two moved here how much will the third Mass move so those sort of questions can be solved using this particular equation okay most of the questions uh you will see are also going to be that kind like the one over here see this there are two masses 10 kg and 30 kg they are along a line and then 10 kg is moved by 6 cm towards the other block how much will the 30 kg move assuming the center of mass of the system is unchanged assuming the center of mass is basically unchanged okay come on my dear Warriors think about it okay what can I just do to qualify s Andes attend this class class concentrate on heavy weightage topics just qualify means 120 marks safe safe score but sometimes 110 100 will also do but on the safety side 120 that means 40 marks per subject that means bare minimum 10 questions should be correct if you have tendency to make mistakes that means you should solve around 13 questions so maybe three questions go wrong here and there so around 9 93 percentile you should get okay 92 sorry you should get cool all right so let's see how do you solve this particular question as you can see the 10 kg Mass the 10 kg mass is moved towards the other mass by 6 cm 6 cm and that 30 kg mass will be moved by some amount which I do not know I'll call it as S2 in fact that is what is asked it is clearly mentioned that their Center of Mass is at rest so M1 S1 + M2 S2 will be zero so Mass 1 is 10 distance is 6 Mass 2 is 30 distance I do not know so from this 30 S2 will be - 10 * 60 30 goes with 60 2 times so - 10 into 2 which is - 20 don't worry about the negative sign negative means it is towards the left side by 20 cm sign is given means it is Direction that's all so the answer is uh did we make any mistake oh it is in meters so oh no it is in centimeters only did we do something wrong I think some factor of 10 is missing just check this out Mass one 10 kg another Mass 30 kg okay 30 and uh oh I know what I did H 6 into 10 is 60 there was no need of putting that 10 I'm so sorry guys it was already 60 had already multiplied it so this would be just minus 60 so S2 will be just minus 2 yes so minus means it is towards the left and by how many cm 2 cm yes so 2 cm towards the other block that is the correct answer which is option C very good okay yes yes yes it was 10 into six I had already written it down correct okay moving on to the next question there is a disc of mass m with surface mass density as shown the center of mass of the quartal dis only only this part is asked the coordinates are this and this what is that x value in the nearest integer very nice question this is like the sector this is like that sector come on like the pizza slice 100% the center of mass will be on the angle bis sector somewhere over here maybe this is where the center of mass will be this is let's say the distance D and the distance D can be found out by 2x3 R sin Theta by 2 by Theta by 2 formula is the radius given I think the radius is given oh radius is given to be a yes the radius is given to be a so a will be here what is Theta observe carefully this is Theta and this complete angle don't ignore this Theta over here which is basically 90° or Pi by 2 so hence it will be nothing but s of < by 2 by 2 Theta itself is p by2 so this Theta should be < by2 by 2 okay so what do I get 2 a by 3 sin of < by 4 sin 45 is 1 by < tk2 okay into this will be pi Y 2 by 2 is 4 so 4 goes on the top so this will become 4 2 8 8 a / 3 < < tk2 that is what that distance from the center will be but that is not the question see this distance I know okay this is your x-axis this is your y AIS by symmetry this will be at 45° and the x coordinate and y coordinate is asked so this will be the x coordinate of the center of mass and this will be the y coordinate of the center of mass obviously because it is 45° this distance and this distance will be equal so X CM will be equal to Y CM which will be how much this cos 45 or sin 45 so D cos 45 or sin 45 is one and the same thing which will then be D value is over here which is 8 a by 3un < tk2 cos 45 is 1 by < tk2 1 byun2 into 1 byun2 is 1 by 2 so 3 piun * 2 8 goes with 2 four times so 4 a by 3 Pi so 4 a by 3 Pi I think the value of x is going to be four yes the answer is four perfect that's it that is the correct answer love the question guys amazing yep very good very good awesomeness is not the area that is what is given in the question no is it no a is the radius uh oh a is an area a is an area as shown in the figure oops then how come we are getting that answer if a is the area I think while marking the they have marked it as the radius but while finding the answer also they have taken it as the radius but if you find it in terms of area then how you will have to do it is means you'll have to say area is equal to Pi A S as per the variables given so a will be a by pi the whole thing under the root that you have to put but doesn't seem to be right so I think this is not the correct assumption it should have been a is the radius of that shaded figure something like that it should have been so I don't think this should have been here so I'm just removing it because the answer is perfectly matching I think there was some mistake while printing it over here is the radius of the shaded figure that's what it should be okay all right all right if anything explodes uh Sanjay then what will happen is basically you know the center of mass will St Inta again you can use the same formula which I have given over here one Mass moves this much other mass will move how much first mass moves S1 other mass will move S2 if there are three particles then you can find S3 if S1 and S2 is known so for explosion problems also you can use this because Center of mass will stay there because the explosion force is an internal force not an external Force so external force is still zero so this is applicable is that okay all right moving on to another question coming up on your screen here it is yes this is more than enough ramchandra but also attend my mock test which we are doing every day yeah what is the answer for this particular question my dear students if there is a truncated body you are removed this part then find the find the uh mass of the center of mass of this following remaining thing the radius of the original dis is smaller okay so let's see this the original disc this particular distance okay this particular distance is basically R so this whole thing obviously is going to be R so the center of mass of that big disc is over here this is where the center of mass one is the smaller Mass which has been removed is this one okay and the center of mass of that smaller Mass which has been removed is over here and that distance as measured from the origin if this is R this will be R by 2 okay now the Shaded part the center of mass will be somewhere over here so we have to find this so X coom will be nothing but as simple as M1 X1 here M1 and then you have minus M2 X X2 minus M2 over here that's what it will be when the masses are not given that's the problem and these are nothing but what is it diss okay so for a disk which is a planer body the mass per unit area will be constant so use that concept now so mass per unit area will be the same everywhere so if I take the big disc the mass is M1 the area of that big disc would have been Pi r² this will be equal to that small disc which was taken out the mass was M2 upon the area will be pi r by 2 whole s so Pi Pi R S R square cancels so M2 / 1X 4 will be on this side equal to M1 divided 1 so what is the value of M2 going to be M2 will be 1x4 goes on the top it will be M1 by 4 or M1 will be four * of M2 one and the same thing so you can put four times that will be easier I think to solve so mass number one will be four * of M2 okay four * of M2 into X1 coordinate of the center of mass of the big disc will be at the origin so into zero okay this again M1 is nothing but four * of M2 minus M2 below here minus mass number two as it is coordinate of the center of mass of the smaller dis is R by2 so R by 2 over here so let's see now what do we exactly get this is zero minus I can see very easily M2 M2 M2 cancels out everywhere so I'm just left with minus r by2 divided 4 - 1 so - R by 2 by 3 so 4 - 1 is 3 so - R by 6 so this coordinate is R by 6 that should be the answer correct minus r by 6 perfect we got it that's how you solve these kind of questions is that okay everyone awesome all right all right moving on moving on to the next one hey lunch break hold on man I'll give you hold on collision Collision related questions all right so all for Collision remember if net external force is zero then the total momentum initially will be the total momentum finally that is one thing okay momentum is always conserved momentum is always conserved that is a standard fact even in explosion but it is the energy which may not be conserve and for that you have something called as the coefficient of restitution so the coefficient of restitution e is given by relative speed of Separation after the Collision upon the relative speed of approach before the collision and this value of e will decide whether energy is conserved or not so when e is one that means numerator is equal to denominator that means approach is equal to the separation relatively relatively then the initial energy is equal to final energy and then there is no loss that is the first particular scenario that you can have the next scenario is where e is less than one but more than zero it is called as inelastic collision inelastic collision here the final energy is less than the initial energy there is some loss there is definitely some loss which is going to happen by the way this Collision was completely elastic Collision the last is basically a perfectly inelastic collision perfectly inelastic collision where e is equal to Z so after after the Collision they usually stick together they usually stick together and the final kinetic energy is obviously less than initial energy and there is maximum loss of energy there is maximum loss of energy so these are the things which you should consider while solving Collision problems not just that sometimes there might be questions on impulses so impulse remember is change in momentum impulse is change momentum and the quantity is a vector quantity so it is actually final momentum minus initial momentum but sometimes you can find the momentum by graphical or integral methods where you might be sometimes given a graph of force with respect to time and maybe that graph is something like this then if you consider the area under the force versus time graph that integration which is force with respect to time that from T1 to T2 will also be the impulse so it is nothing but area under the force versus time graph remember whatever is here will be positive area this will be negative area this will be positive area whatever is on the top is positive whatever is below is negative sometimes there can be impulse related questions also all right so let's solve some questions now here it comes okay first question only graphical question 2 kg Mass is at rest a force acts on it magnitude changes with time the force time graph is as shown below what's the velocity after 10 seconds see if this was force with displacement I will calculate work and I will use work kinetic energy theorem but if it is force with time I will do it with the impulse method I will do it with the impulse method got it awesome so how do we do it okay come on come on everyone gji from Andra some of you are from Tamil anandu very good anybody from Karnataka anybody from Kerala Maharashtra please let me know quickly in the chat box while you're answering thank you AR Sanjay thank you so whenever we have Force time graph we will obviously find the impulse let's start with finding the area first okay so there are too many areas over here so let's go step by step uh I mean first things first this one it's a small triangle it will be half into base into height which will make it 10 this is a rectangle 2 into height which is 10 which will be 20 okay then again this is a trapezium so trapezium means half into parallel sides addition so height is 10 one side is 10 another side is 20 so 10 + 20 into the distance between the parallel sides which is nothing but two okay so this will be 10 + 20 is 30 2 two cancels so this is 30 this area will be half into base which is 4 into height which is 20 4x2 2 2 into 20 is 40 so what is the total area then it will be 10 + 20 + 30 + 40 10 + 20 30 30 + 30 60 60 + 40 100 so 100 is the complete area Okay so once we have this we can do the next part uh impulse is change in momentum impulse is nothing but the area under Force time graph which is 100 change in momentum is nothing but final minus initial momentum final momentum is mass into final velocity initially it was at rest clearly mentioned over here all right so therefore VF is 100 divided by 2 hence it will be 50 units so I think it should be answer D yes it is correct very good option number four option number D awesome thash happy Pongal Jin happy Bal disaster very good Sachin very good anandu very good herbine awesome awesome tan awesome very good Girish Ashwin thank you for all the love from Tamil Nadu disaster okay shall we go ahead to the next question then here we come 50 g bullet moving with some speed gets inside another body how much is the loss of kinetic energy of the system that is the question all right so first of all uh let's draw the diagram this is essentially 50 g and it is moving with 10 m/ second there is a big box which is let's say at rest and the mass is 950 G after the Collision after the Collision what will happen it will just become one big thing with the bullet inside okay and it gets embedded in it this will become 1,000 G 950 + 50 is 1,000 and it will now move with a new velocity so yes it is a perfectly inelastic collision but momentum is conserved so Mass into velocity plus Mass into velocity it is at rest is mass into velocity so this will become basically 500 isal to 1,000 V so V will be 500 by 1,000 which is basically .5 m/s now that's not the question the question is find out the loss in the energy percentage loss so percentage loss will be initial kinetic minus final kinetic upon initial kinetic into 100 that's the change upon original change upon original is the loss of the percentage energy initial kinetic energy is half mass is 50 g into velocity is 10 squ minus final kinetic energy is half 1,000 g into velocity which is5 squ whole thing divided by half into 50 into 10 squ this whole thing into 100 now I know some of you will be thinking sir why did you not convert the GRS into kg yeah I could have but it is unnecessarily going to be meaningless because like sir how can you multiply grams with meters per second I know technically I shouldn't but I have a smart move here I know if it is grams here grams here grams here eventually it will get cancelled eventually eventually it is going to get cancelled so I don't really care whether it is grams or you know pounds or some other quintals or tons also okay I hope this is absolutely absolutely clear so therefore I can solve this easily now half half half cancels out 50 into 10 squ so two more zeros minus. 5 square is 25.25 so 0.25 that means it will become 250 over here whole thing divided by half has got canceled out so 5 Z and two more zeros into basically 100 so 5,000 minus 250 okay by the way these two zeros these two zeros will cancel 5,000 - 250 is 4750 divided 50 0 0 cancels 475 475 divided by 5 come on my dear Warriors 475 divided by 5 how much is it going to be how much is it going to be 9 five yes 95% just check this out 95% that should be the answer yes that is the correct answer that's how you solve this very nice these kind of questions are very very common this is also very beautiful question where there is a block it's coming towards another rest block which has a spring attached that block hits the spring the spring will start compressing and the question is what is the maximum compression right now what's the speed it is 2 m/s this block has 1 kg and uh the rest block each of the blocks has 1 kg okay even this has 1 kg eventually what will happen is eventually what will happen is this spring would be compressed by X this has been compressed by X and because this is maximum compression maximum compression that means both the velocities will be equal now this is a concept which many people take some time to understand also why should maximum comparation means velocities are equal see think in terms of relative velocity imagine you're sitting on this block you will see you are at rest on this block the other block is coming it hits me so I start moving that's okay I don't realize my motion but for my relative motion that block will come close close close close close stop and then it will start moving away so that block from the back is coming and going behind so when it stops that's when the compression is maximum when it stops with respect to me when that block comes and stops with respect to this Observer it stops means relative velocity is zero that means both velocities will be same so very very crucial thing so if one considers relative motion the relative motion is zero at maximum compression at maximum compression hence therefore both of them have same velocity then both of them will have the same velocity during the maximum compression got it everyone yeah so what energy went into what energy it's a question on energy conservation now you can see there was initial kinetic energy there was no spring potential energy at all it went into final kinetic energy and some spring potential energy initial kinetic energy is half Mass into velocity Square nothing else is there finally both the masses have the same energy half into 1 into v² but two times why two times because there are two blocks spring energy half K spring constant is 50 so 50 * x² you just have to Sol all this now it's not that difficult 2 s by 2 that's going to be just 2 is equal to 2 two cancels so you just have v² oh but wait a minute I don't even know v² plus 50 by2 is 25 into x² problem is what the hell is this V oh now comes the logic of momentum conservation momentum has to be considered spring is an internal Force yes momentum can be conserved net external force is zero so momentum is going to be conserved is going to be conserved so initial momentum is mass into the velocity the other block was at rest other block was at rest over here finally both the masses move together so mass is 1 into V plus mass is 1 into V so therefore 2 is equal to 2v therefore V is equal to 1 oh so that's how I get the velocity substitute it back over here substitute it back over here so 2 is = 1 2 + 25 x² so 1 2 - 1 is 1 is = 25 x² so x² is 1x 25 so X = 1X 5 of a meter so X is = to 20 cm so 20 cm or 1X 5 m or 2 m everything is the same thing got it everyone uh electrostatics or Ray Optics Ray Optics as compared to electrostatics is little smaller electrostatics needs even more knowledge okay of other chapters like energy work Newton's Laws vectors all that re Optics completely independent re Optics is also being electrostatics is also big if you consider gos and all of that and it has many more Concepts than re Optics re Optics is that way simpler than electrostatics but some people might differ in opinion they will be like no sir I find electrostatics easing that's because you have done gravitation properly in 11th standard that's the only reason or maybe you know the basics very well okay all right can you do it by reduced Mass concept yes you can do it but it might be often confusing how to use that concept when you don't have complete understanding of it then okay the next concept of moment of inertia moment of inertia is the equivalent of mass but in rotation and it depends on three things how much mass you rotating which axis about you rotating which axis is rotated okay and third thing how far are these masses from the axis maybe the axis is same the masses are close or far apart if it is far it is very difficult for it to rotate if the masses are close it's very easy to rotate so it depends on all these three factors and it is the equivalent of mass but for rotation the formula is Sigma summation Mass 1 R square Mass 2 R square every Mass multiplied with the distance from the axis of rotation you also get a concept of radius of gation which is if there is a body which is rotating every Mass is at different different place so you find the moment of inertia of that big body radius of gation is that particular place or that distance from the axis where you can combine the entire mass of the body into a singular point and it will possess the same moment of inertia so you smelt the entire body condens it into a point mass and you rotate it along the same axis so that distance which will give the same inertia is the radius of gation so radius of gation is again MK Square okay so radius of gation is given by the formula MK Square K is the radius I is the inertia m is the mass cool these are the main things all right all right perfect now now standard moment of inertias of standard bodies you should know this like for a ring Mr Square for a disk Mr Square by 2 for a rod when it is rotating about Center yes a rod about the center ml Square by 12 but if you take it and spin it about the end using parallel axis theorem you get it as ml Square by 3 be careful all right then if you have if you have a solid sphere it is two 2x 5 Mr s if you have a hollow sphere if you have a hollow sphere then it is 2x3 Mr s 2x3 Mr squ keep that in mind then if you have a rectangular plate imagine a plate and that plate is rotating about a axis perpendicular to the plane then it is ml s by sorry M by2 A squ + B sare height length Square you can add it that's the formula for a plate which is rotating now now if there is any other axis you have no other choice but to use the uh you know theorems one is parallel axis one is perpendicular axis theorem so first is that parallel axis theorem which says that moment of inertia about parallel axis is moment of inertia about Center of Mass plus the mass of the body multiplied by how much you are shifting it by square okay so this is the first Formula so if there is a mass here this is the center of mass maybe I know the moment of inertia about this axis so moment of inertia about Center of mass now you want to rotate it about this axis so this is the parallel axis that means you have shifted it by this much distance so this is the Distance by which you have shifted it that's how you can use this formula the next one being the perpendicular axis theorem where you can only apply it to planer bodies or laminar objects planner planer means two dimensional bodies only so maybe I rotate it once about this particular axis let's say the moment of inertia is i1 then I rotate it about this particular axis the moment of inertia is let's say I2 this may be center of mass may not be center of mass doesn't matter Center of mass concept only comes for this not for this you draw perpendicular axis perpendicular means like this okay go like that so this perpendicular axis moment of inertia will be the sum of i1 and I i1 + I this is called as the perpendicular axis theorem got it so perpendicular axis theorem only for planer objects parallel axis theorem only it can be for any object but one of the axes must pass through the center of mass here there is no such condition for Center of mass keep that in mind okay Perfecto can I take take a screenshot definitely Rakesh why not you can definitely take a screenshot let's see if you can solve this question come on try to solve this question the value is 2 is to rootx what is the value of x root X has shifted here some formatting issue all right so let's do this uh what is it solid sphere and solid cylinder for a solid sphere the moment of inertia formula is 2x 5 m r² if I equate it with M K of that solid sphere solid sphere Square mm will can cancel K of that solid sphere will be R root of 2x 5 similarly if I find the moment of inertia of that solid cylinder of that solid C cylinder it is the same as Mr s by 2 which is like a disk this I can write it as M uh what is this radius of gation of that cylinder Square mm cancels so K of the cylinder will be R by < tk2 the question is all about the ratio of this so K of the sphere by K of the cylinder just take these two things and divide it R root2 by < TK 5 ided R by < tk2 r r cancels < tk2 will mply with < tk2 and I will have rooot 5 here < tk2 into < tk2 2 so 2 byun 5 so this should be obviously root5 hence that x value is five perfect that's the correct answer cool many of you gave the answer as five very good Theos very good nagri very good shasa awesome awesome Asif how much time my God I don't think we have even reached half of the session I hope you agree with this yeah can you tell the conditions for with and without slipping uh the beta values K I'll just tell you with or without sleeping what do you mean by Beta values you mean you are asking the condition for sleeping and not sleeping see if it is not sleeping simple V is Omega R and the point of contact not does not move with respect to the ground at that instant if it is slipping V will not be equal to Omega either it will be more or less and the point of Quant will have a relative motion that's all choose the correct answer moment of inertia solid sphere about any tangent oh my God everything is about some axis which is different so moment of inertia of a solid sphere about a tangent I know about the center of mass it is 2x 5 Mr r² so plus I have to shift it by R so plus Mr r² because this is the tangential axis and this was the center of mass so that will be 2x 5 + 1 is 7x 5 m r² and just check this out yes 7x 5 Mr R square so a definitely a definitely goes with this option two is that right everybody with me on this clear okay next yep next a is going with two so automatically D option gets eliminated and even B option gets eliminated because a is with two is only there in the two options now B is with one so both the options will give me again that confused result but C option or D option can give me Clarity C option is moment of inertia of a ring about tangent and moment of inertia of a disc about any diameter anything you can go let's say go with the D option so for the D option moment of inertia of a dis about any diameter so if you take a dis this moment of inertia I know it is Mr s by 2 about the diameter I do not know let's say call it ID any diameter these two axes are in the plane and it's a 2d object I can use perpendicular axis theorem so it will be ID plus ID therefore Mr r² by 2 is two times of ID or ID is m² by 4 Mr r² by 4 is third option so D will go with the third option D will go with the third option which is over here so this can't be correct this automatically gets eliminated so C option is also eliminated so hence answer will be a hence the answer will be a so that's how easily you can solve match the following you don't have to sit and solve every option just see which options are leading to Clarity it should not lead to confusion I hope this is very very clear very nice awesomeness let's move then to the next question coming up on your screen yes angular momentum conservation comes many times remember angular momentum angular momentum if you take for a particle the formula is mass into R distance from the axis into the velocity but if you take angular momentum of a big body which is many particles it is moment of inertia into angular velocity now if it happens that from outside the external torque is absent then then then angular momentum is conserved angular momentum is conserved that means the total angular momentum initially will be the total angular momentum finally usually it might happen like disk dis problems are there a dis is touching another disc and all of that so or a moment of inertia has changed so i1 Omega 1 will be equal to I2 Omega 2 these kind of problems can come in your examination there is a person who is holding his hands close by inertia's eye he stretches his hands moment of inertia becomes double so if inertia becomes double angular velocity will become half so those questions are also again standard questions all right let's see some questions on this there is a disk of inertia I and it's perpendicular to the plane it is rotating with om GA speed another dis 2 I rotating with double the speed in opposite direction if they are combined together what's the final speed what's the final angular speed how to find Ang moment of inertia of truncated bodies exactly the same way as Center of mass just i1 minus I2 just i1 minus I2 so basically if you uh ask me over here moment of inertia of truncated bodies imagine there is a body here like this and from that you have taken out this particular body so this body about let's say maybe this is the axis about which you're rotating it if you know the moment of inertia of that big body it is i1 and the cavity which is removed about this axis is I2 then whatever moment of inertia is there of that remaining shaded figure over here right that moment of inertia will be simply put i1 minus I it will be just i1 minus I2 just the essential condition is everything about the same axis about the same axis you cannot change the axis for the yellow thing the axis is not this the axis is this so you might have to use parallel axis theorem and all of that okay so most of the times it involves parallel axis theorem so keep that in mind okay the should be the same for everything okay all right let's solve this question which I just gave it to you all right so let's draw the diagram it will be very easy imagine a disc of moment of inertia 2 I and it is rotating like this with 2 Omega another dis is of moment of inertia I it is rotating with Omega now you combine both of them okay so basically what happens is one dis will be on top of another disk the moment of inertia will be three bi and this is higher speed higher inertia so that will dominate so this will be the final angular velocity so conserve the angular momentum that's it conserve the angular momentum initial angular momentum will be I into Omega this is the first body's angular momentum I into Omega for the second body both of them are opposite in direction so put minus okay why is this minus they are in opposite directions that's the reason for it so this will become four this will become 1 so this will become 3 I Omega this will be equal to on this side total moment of inertia 3 I Omega 3 I into Omega final so this will be 3 I into Omega final so what will Omega final b i i cancels I think 33 also cancels it will just be Omega wow yeah so that is the answer the answer will be Omega I think the answer was not printed but yes the answer will be just Omega is this absolutely clear everyone till this point shall we move ahead okay very good let's move next question yes gravitational force energy and uh Escape speeds awesome let's go first of all gravitational force between two masses gravitational force between two masses is very similar to electrostatic slope and that force is given by G M1 M2 by the separation Square it's like the inverse Square law right now if you if you find the gravitational field due to gravitational force the field is the force by mass just like the electric field so gravitational field I think the symbol used over here is wrong don't use this symbol use e gravitational field is force per unit Mass it is GM by r² that is why the unit also will be Newton per kg yeah gravitational field will be the force acting per unit Mass the properties of the field are very similar to electric field concept or magnetic field concept okay so it will the field will give me the direction of the force acting on a unit test mass and all of that now next concept if there are two masses if there is an interactive force it will also have an energy between them the intera energy of two masses which is also called as a gravitational energy is given by negative G M1 M2 by R not R squ if it is R square it will become Force if it is energy it will become R keep that in mind negative energy very important only for Gravity for electrostatics that negative sign does not come in fact these negative signs only come when the forces are attractive even in electrostatics if you have a positive and a negative charge the total energy becomes negative if you have two negatives or two positives it will automatically become positive potential energy is that okay okay yes lunch break CI lunch break will be given just one second let me just complete gravity okay after gravity we'll have lunch break what's say guys yes all right all right now just like any other problem you can conserve energy so uh Whenever two planets one planet one Sun One Planet one Moon anything two heavenly bodies are moving towards each other or you throw a mass whatever you can use energy principle you can use this potential energy formula to find out anything to find out kinetic energy speed Etc and once such calculation is done for escape speed meaning you throw a mass from the surface of the planet and it should never ever come back that means after it goes to Infinity it should stop that means when it is very very far away kinetic energy becomes negligible so that speed with which you should throw so that it never comes back is the escape speed which is < tk2 GM by R and this happens because as it goes towards Infinity as it R tends to Infinity then the potential energy of infinity becomes zero and the ktic energy and that Infinity also becomes zero this R is don't confuse this is not not the radius of the planet this is the distance from the planet this R is the radius of the planet this is the mass of the planet Escape speed is independent of the mass of the object very very important it is also not dependent on the angle at which you throw it yes 3 Pi lunch break after this particular thing okay very cool ninja yes I know some people what to do they think that if you delete the chat I cannot see a I can see the chat man the admins also can see the chat the not just me the admins who are behind also can see the chats okay let's solve there is some Mass taken from the surface to a height equal to double the radius of the planet the change in the energy will be how much where G is the acceleration due to gravity on the surface okay so this is the planet this is that radius earlier the mass was here and now you have taken it to a distance of 2 R and you have brought it over here so this is the initial point this is the final Point what is the change they have asked initial energy well the mass is separated by distance of R so it will be G mm ID R finally it will will be g m m the total separation will be r + 2 R which will be nothing but 3 * of R from this I will get the change in the energy which is final minus initial so minus G mm by R is common so 1 by 3 is over here minus 1 by 1 is over here that's it is that right minus oh minus sign is all already taken common so no need of doing that minus one is over here okay so this will become minus GMM ID R 1X 3 - 1 or 1 - 1 by 3 is 2x3 so this will be minus 2x3 okay minus minus becomes plus so it will become 2 GMM divided by 3 * of R but none of the options are matching what to do no issues we know one more thing on the surface the acceleration due to gravity is GM by r Square so GM is basically gr r² so use this substitution over here so this will become G r² rest of the things as it is so 2 m over here divided by 3 R RR gets canceled and I'm left with 2G M divided 3 so 2x3 MGR 2x3 MGR is right as option C yep very good awesome happy Pongal MTI happy Pongal happy Pongal yeah why can't we use U is equal to MGH Girish you only tell me why we can't use MGH what is the problem many people will use that I know why we can't use because that formula is only valid for small Heights G should be constant when you go for a height which is double the radius of the planet do you think G will be constant no right so that formula is only for few meters maximum 2 3 km 10 kilm okay but when it is thousands of kilometers you can't use it next Escape speed of two planets are in the ratio 1 is to2 If the ratio of the radar respectively is 1 is to3 then the ratio of the acceleration due to gravity of Planet a to the acceleration of Planet B will be how much yes come on let's try to solve this Escape speeds ratio of radi ratio of the acceleration of the planet a so acceleration of Planet a upon acceleration of Planet B will be G mass of a by radius of a squ by G mass of B upon radius of b² GG cancels so it will become M A by MB and it will become RB by R A the whole Square I think the ratio of the rad is given to be 1 is 3 so this is one this is three this is squared I just don't know Ma by MB no issues we can use this information Escape speed of Planet a by Escape speed of Planet B will be root of 2 G mass of planet a by radius of Planet a upon root of 2G mass of planet B by radius of Planet B okay Escape speed ratio is 1 is2 so this is 1 is to 2 GG 22 cancels so it will become root of 2 * mass of a upon mass of B and here it will become RB by r a the ratio of the radii is 1 is 3 so this will become 1 by 3 this will be root of M A by MB this is nothing but 1 by 2 therefore mass of a by mass of B whole thing under the root will be 3 comes below so 1 by 2 < tk3 therefore mass of a by mass of B will be square of this so 1 by 2 s < tk3 Square will be 3 so 2 sare is 4 4 3 are 12 so 1 by 12 over here okay so ma a by MB is 1 by 12 so how much will this come out to be so 3 square is 9 so 9 by 12 9 by 3 is 3 12 by 3 is 4 so 3x4 which is D option correct that is perfectly fine got it my dear students so it's a slightly lengthy problem but it is a good problem it is a very good problem very good awesomeness awesomeness next question radius of the Earth and the acceleration r g is equal to Pi Square then the length of the second pendulum at height equals to 2 R will be how much very interesting question very good radius of the Earth is R acceleration due to gravity on the surface is G what is the length of the seconds pendulum when the height is 2 R now remember for a seconds pendulum when you use the time period formula for a pendulum which is 2 piun L by that g G at that height I just need to find out how much is this length because it is given to be uh seconds pendulum the time period will be 2 seconds so just put two here this is pi I don't know L what is that gravity at height H the gravity at height H is given by the formula G r² by r + h² so G is g r is R okay R plus actually G is not g g is given to be Pi square look at that so it is pi Square r sare as it is r + H H is 2 R so this is 2 R whole squ so this will be < S r² 1 + 2 3 3 square is 9 so 9 R square R sare R square cancel so it will become < Square by 9 so put this as < sare by 9 what will happen Pi Square becomes Pi Pi Pi cancels so I will be just r with N 9 * of L which is 3 * of root l so root L will be 2x 3 therefore L will be 2 s by 3 S which is 4 by 9 which is 4 by 9 which is D option I think 1 by9 was wrong uh just check this out it should be 4X 9 off a meter yes everyone yes 4x9 awesome awesome yes it should be 4 by9 not option A yes the math session will be there tomorrow or day after tomorrow so next two days is chemistry and Mathematics yes perfect oh I think I made a mistake somewhere yes I know where I have made the mistake that number two I'm so sorry guys this time period was 2 seconds so this is is 2 Pi root of L which I don't know by GH GH was < s by 9 2 two cancels so I'll be getting 1 is = piun < TK L * 9 < square < square Pi Square cancels so it will be root of 9 L so 1 square will be 9 L therefore L will be 1X 9 M so I think this should be the correct answer then yes it is perfect yeah I think I didn't cancel the two before yep how time period became 2 seconds seconds pendulum seconds pendulum means what it goes like this take and it goes like this talk so tick is 1 second talk is 1 second so tick talk is 2 seconds that's the second spend got it Sachin Paka yeah awesome next satellites and Kepler's Law after this we'll quickly have a break satellites and Kepler's Law let's quickly revise the formulas for satellites the velocity of that particular orbit will be given by root of GM by R where R is radius of the planet plus the altitude that's the formula for velocity of the orbit the time period of revolution the time period of revolution is given by 2 Pi root of small R Cub by GM this is a time period of revolution remember one thing if if the velocity is not equal to the velocity of the orbit then the path is going to be elliptical then it is going to be an elliptical path then it is going to be an elliptical path this is assuming the velocities are still lesser than the escape Velocity if by chance the velocity is equal to Velocity is exactly equal to the escape Velocity then the path taken by that body around that planet will be exactly a parabola Parabola and if by chance if by chance the pl velocity of the object is more than the escape Velocity then the path taken by that particular body is going to be a hyperbola these are the things which you should remember and only for this particular speed it is going to be a circular orbit otherwise it will be ellipse Parabola hyperbola depending on where the speeds are also keep in mind certain more things when you have the time period of that revolution of that satellite is equal to 24 hours it is called as a geostationary satellite geostationary geosynchronous satellite when that R is nearly r that is H is very very small then that is called as a surface satellite surface satellite okay these are the two terms which you should be aware of next Kepler's laws if you talk about it if this is the Sun then the planet will go the planet will go in an elliptical orbit such that the sun will be at one of the focus this is the first law of Kepler this is the first law of Kepler the second law says the second law of Kepler says while it is going in the elliptical orbit when it is very close the speed will be more when it is very far the speed will be less that's because the area which it sweeps per unit time is L by 2 * of M which is going to be constant L is the angular momentum angular momentum which is conserved angular momentum is conserved so L by 2m is constant so the area which it covers per unit time is same so when it is closed it will move more so that it will be the same as the area when it was far away when it is far because this distance is more it will move less so it will be fast over here and it will be slow over here obviously at this point you have the sun okay this is a second law and then comes the final law which is the third law of Kepler where the time period of rotation square is proportional to the radiuses cube this is also there over here if you square this t² will be proportional to R CU okay this is the third law of keplar yes I know Tik Tok is banned but Tik Tok pendulum is not banned seconds pendulum is not Bann luckily so we can use it in J Okay match the following I think energy kinetic energy potential energy formulas you should know this come on quickly figure this out total energy of a satellite total energy of a satellite is minus GMM by 2 uh whatever a if you talk about potential energy it is minus GMM by a and if you talk about kinetic energy it is G mm by 2A you can see kinetic energy is negative of total energy and potential energy is double of the total energy so similar to Atomic Structure electrons revolving around it so everything is there over here come on guys which option is matching first option A will go with three kinetic energy of the planet G uh sorry a will go with two my bad GMM by 2A perfect then B will go with one gravitational energy of sun Planet system yes minus GMM by total energy of the planet c will go with four which is minus GMM by 2 a which had written down over there minus GMM by 2 a Escape energy of the surface of the planet of unit mass that will be nothing but GM by R perfect everything is matching nothing problematic yes these are the formulas which you should know these are for satellites exactly similar to electrons in orbits okay planet takes 200 days for revolving around the Sun if the distance is made 1/4 then how many days will it take Third Law of Kepler nothing more t² proportional to the cube of the radius so the new Time Square by the old time which was 200 square will be the new distance it is 1/4 of the original distance so R by 4 q original distance was R that's what it will be so r r cancels 1X 4 CU 1X 4 CU 4 4 are 16 16 4 are 64 is T new Square by 200 squ so T new Square will be 200 squ by 64 so the new time period will be taking Roots it will become 200 root of 64 so that will be 200 by 8 what is 200 by 8 100 by 4 which is 25 yes so that is 25 days which is D option it is a d option perfect very good awesome yes you started the live at 11:00 in the morning all right so we'll come to this after the break okay so we'll have a break time wow that's a little bit late lunch break but it's okay let's meet after 20 minutes e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e welcome back welcome back I just had some nice Pongal and uh I don't know what you guys had just quickly let me know how was it yes let's start banunga sir yes we are starting started started started all right the lunch break is over time up and we are on to solids and after this I think Thermo is there a little bit of waves concept and we go to the 12th standard important Concepts too sweet Pongal Pongal only sir Pongal sir wow super super ghi all the students out here quickly let me know what you had for lunch yes and call your friends back because St s is starting the next segment after the lunch break and we are on to solids now I think you would have already seen through the slides but let's quickly go through the slides again let me tell you when we start this particular concept of stress TR and all of this remember in general any kind of stress is nothing but the intensity of the force which is force per unit area and the strain is uh basically you know the change in the length upon the original Dimension upon the original Dimension that is what it is and the modulus and the modulus of elasticity the modulus of elas city is given by your stress your stress divided by strain stress divided by strain so the unit of modulus of elasticity will be pascals or Newton per met Square this is dimensionless and this is also going to be in pascals remember there are three different kinds of deformation that's why you get three different kinds of stress strain and modulus so one is basically longitudinal deformation longitudinal deformation where the longitudinal stress is the perpendicular Force by the area The Strain is the change in the length the strain is the change in length by the original length and here you get Young's modulus which is that stress divided by the string similarly you get sheer def formation where you have sheer stress as the parallel Force by the area when I say parallel and perpendicular what do I exactly mean see when you have an area when you have an area the force can be at an angle maybe the force can be at an angle when I say perpendicular Force it's this component of the force and when I say parallel Force I mean the force which is parallel to the surface that's what I mean okay so Shear means this kind of deformation you are applying the forces parallel to the surface it bends it deforms and the strain will be the uh you know the motion along the surface upon the height between those two surfaces that's what it is and that is also tan of theta and here you have rigidity modulus which is the stress of Shear upon the strain which is X by h lastly you get the bulk deformation bulk deformation where the stress is the change in the pressure this is useful for volumetric deformations you expand a gas you compress a liquid you change the volume of a solid those kind of things the strain is the change in volume upon original volume and here you have the bulk modulus which is change in pressure upon change in volume upon original volume but it comes with a negative sign here that's it yes I hope this is absolutely clear yes usually the 11 physics theory is very vast although the weightage is very similar thank you thank you only J for all the Telo people yes thank you so much thank you so much all right okay now all this is given here also nothing different uh few more formulas which you should know is the energy density so the energy stored per unit volume is given by half stress multiplied by strain also the equivalent spring constant of an elastic body is given by Young modulus into a divided by L you can use this so when you have elastic body you can convert it into a spring like structure of equivalent spring constant y a by L you can use f is equal to KX where that K will be this or time period formula where the K value will be this all these are valid and remember that uh you also need to go through the stress strain graphs which is done many times where in the beginning you will see in the beginning you will see that the stress is proportional to the string this is where the hooks law is valid hooks law is valid and here stress is proportional to the straing and the slope of this graph often gives you the young modulus till a particular point this is called as the proportional limit after this it is not proportional rather it is just elastic in nature that means if you release it it will come back to its original state and shape till this particular point which is also called as the elastic limit and this particular stress till which you can give it is called as the yield stress till this point it is basically elastic in nature after it becomes inelastic that is over here then it is not a two-way graph you can expand it but if you release it it will probably come back over here if you expand it till here and release it it will probably come back over here this is basically your permanent deformation this is basically your permanent deformation or permanent set this is your plastic Behavior this is basically your plastic behavior and this happens till a particular point which is often called as the maximum load which you can give so this is also called as the strength of the material the strength of that material this is the maximum loading point which you can load it till because after this what is going to happen is the irreversible damage it is just going to decrease the stress and it will eventually break or basically it will fracture there is it is irreversible you can't come back you can't go anywhere that's it it will happen very fast this happens very fast these are the things which should know about the stress strain diagram yeah uh yeah ban that's the aim to complete the class before the mathematics class I know so we'll try to complete it by five 6:00 for sure or maybe at least 6:00 okay here is the question the wire of certain length and area is hanging the length of the wire changes from to L1 when the mass m is suspended then the expression for the Young's modulus is how much okay so basically the original wire was having certain length and then the wire became longer over here the original length was L the original length was L and when that mass was hanging over here of uh how much M basically then the length became L1 okay it was supported from the top the wire itself is massless as you can see the extension over here the extension over here is L1 minus L and if you notice the stress on the rod which is the force by area the force is mg and the area is basically a so this is the stress this is the extension this is the original length so we can easily figure out what is the Young's model Young's modulus is stress by strain stress is mg / a strain is x ided l so it will be mg / a extension is L1 minus L and original length was l so mg L by a L1 minus l so that is nothing but option number c c for your captive or Captain sh no it is not B it is option C yeah yeah yes very good yes today we are going to complete it B Raju even if it is late yeah is it okay to write J with only 12th chapters zba if you're planning to only study 12th trust me it is going to be a little bit dicey situation because although it carries 50% weightage but lot of dependencies are there like vectors Newton's Laws work energy shm waves these are chapters which are basics for another chapter like electrostatics electromagnetic induction or gravitation relates to electrostatics and then even AC and even light waves are related on waves and oscillation so so many dependencies are there so if you can tackle that it's okay or else actual weightage might be 50 but what happens practically is it becomes less than 30% so 30% is barely 20 30 Marks here and there and the two you might make mistakes in that so that means you barely might score 20 to 25 marks by just studying um you know 12th standard without knowing anything about 11th that's the problem okay so moving on to the next question there is a catapult made of rubber cord which is some meters long some crosssection negligible Mass a stone is there and he stretches it and releases it it flies off with 20 neglecting the change of area find the young modelist this is a question completely based out of energy conservation how you might ask because because when you stretch it it has elastic energy that converts into kinetic energy so it's just a question of elastic energy elastic energy getting converted into kinetic energy what is the elastic energy well it is the density into the volume density of energy into the volume density of energy into the volume and this is nothing but half Mass into v² now you might ask what is the density density of energy we have seen it is nothing but half stress into string into the volume volume is nothing but area into the length so this is equal to half M v² half and half cancels out stress into strain now I don't think stress is given because force is not given so get rid of stress stress is Young's modulus into string correct because Y is Sigma by Epsilon so Sigma is Y into Epsilon so into Epsilon area area is pi r² into the length this is equal to M into v² speed is given young modulus has to be found this is the strain right okay so this will become Young's modulus into strain square into Pi radius is not given I think diameter of the cross-section is given so it will be D by 2 whole square into the length is equal to M v² all right so next step will be nothing but Young's modulus strain strain is not given but the change in length upon original length can be written down so x² by l s pi and you have D ² / 4 here you have L isal to M v² many things will cancel anyways Young's modulus is asked so four can be taken up MV sare can be taken up and also L will remain because one L will get cancelled so 4 ml v² the whole thing divided by you have pi over here then you have x² then you have d s l got canceled that's it m is known L is known V is known Pi is known X is known D is known everything is known solving this you will get the young modulus okay solving this you'll get the young modulus as same calculations are given 10 to the power six everything can be substituted so 10^ 6 pascals or Newton per M Square got it awesome awesome moving on to the next concept coming up on your screen here it is there is a rubber ball which is taken to the depth of 1 kilometer inside water so that its volume reduces by 05% what is the bulk modulus for rubber that's the question yes today we are completing 12th syllabus also well in this particular question the rubber ball is taken 1 kilm inside so therefore there will be a change of pressure given by row g h density of water 10 the^ 3 G is 10 height is 1 kilm which is 10^ 3 so this will become 10^ 7 pascals now the next concept what is the bulk modulus bulk modulus is change in pressure upon relative change in the volume negative sign but I'm interested only in the mod value anyways so change in pressure 10^ 7 the volume reduces by 05% which means Delta V by V is 05% now if this is percentage think about it actual value will be 0.05 divided by 100 because when you convert it into percentage you multiply by 100 when you relieve percentage you divide by 100 so this will be 5 into 10 power -4 so just put it over here 5 into 10^ -4 so this will become 10 ^ 7 + 4 that's going to be 11 by 5 which is nothing but 1 by 5 is uh yeah. 2 into 10^ 11 which is 2 into 10^ 10 2 into 10^ 10 is C option that is the correct one got it my dear students everybody with me perfecto shall we move ahead to the next question yes shall we move ahead to the next question yeah the concept of fluid mechanics was only limited till here r g this is very easy Leo formula okay let's go some pressure is applied on a cube so that it is compressed K is the bulk modulus and a is the coefficient of linear expansion or Alpha is the coefficient of linear expansion suppose we want to bring back the cube to its original size what should be the temperature change yes you're all right so my dear Warriors coming back to the question now when you apply some pressure it will compress so we can find the change in volume using this formula bulk modulus is the pressure change upon change in volume by original volume so Delta V will be check this out Delta V will be Delta P Delta p k comes below V Will Go On the Top This is what it will be okay now how much is the change in the pressure I think it is given external pressure p is applied and uh technically this was not K usually we use the bulk modulus symbol so this was B so getting it back into original symbols Delta V will be p v divided K as per the symbols given now there is also another formula for change in volume if you notice for thermal expansion for thermal expansion change in volume is original volume gamma into delta T but gamma is not given Alpha is given but we know coefficient of volume expansion is three times of linear expansion so gamma is 3 Alpha into delta T definitely so Delta V from here if I substitute which is p * V / K as you can clearly notice over here volume volume just gets cancelled all right and we have to find delta T okay so if this is the case put 3 Alpha below so P by 3 Alpha K is equal to delt T that's what is asked what is the temperature that should be raised P by 3 Alpha Q yes that's the answer option number c sometimes they can con you know combine it with some another chapter like you are seeing over here so don't think if I just do one chapter will I be able to solve all the questions Maybe but usually when they combine the chapters and you don't have knowledge about something else then you will be stuck in that question so that is the reason why you should not just go through the vitage you should also see how many combined questions can be asked and that's where the magic lice all right all right all right Perfecto Perfecto let's move to the next concept of calorimetry in this again every time most of the times you will see a concept uh uh sorry a question based on this particular concept where you know either they will ask you equilibrium temperature or they will ask you specific heat capacity or they will ask you heat required all these kind of questions are usually asked over here so the major formulas are when you are going to melt or when you are going to vaporize or you going to freeze or you're going to condense then the heat required will be be M into L that's the formula don't use MC delt T because this kind of operation is a isothermal operation that means the temperature is always going to be constant in a phase change so whenever there is a phase change the temperature never changes it's the state solid liquid gas which changes and the formula is ml m is the mass L is the latent heat usually for latent heat from Ice to water is usually 80 calories per gam and the latent heat for water to steam water to steam is 540 calories per gram standard value now when you are in the similar phase liquid to Liquid Gas to gas solid to solid then you use MC delt formula here this is in the same phase that you will use and temperature can change by delta T M is the mass C is the specific heat capacity standard formula specific heat capacity of water is 1 calorie per gam per degree Centigrade that's something which you should know all right I hope this is clear C for yes please ask please ask chapter which is going on we are on to Thermal physics heat Kaa block on block concept not needed I mean it's a low weightage thing for J Advance yes sometimes they ask questions on that but not necessary every single time okay now when you reach thermal equilibrium when you reach basically thermal equilibrium then the temperatures of the bodies a or basically you can say some bodies over here and the temperature of the other bodies on the other side both will be equal and when that happens when that happens I can also say one more important thing that is the heat which is lost by the hot body is equal to the heat which is gained the heat which is gained by the cold bodies so this is very very important because this is the principle of calorimetry so some things will lose some things will gain how much is lost or how much is gain can be used can be found by these formulas ml or MC Delta so see which are hot see which are cold accordingly solve the question that's all okay all right let's do some questions then let's do some questions calor meter water equivalent contains water 25 steam at 100 mixed in it final temperature 31 that's at thermal equilibrium latent heat of water and specific heat capacity given now when you see this word water equivalent water equivalent it is exactly what it means see any object will have its own specific heat capacity meaning if you supply some heat it will raise by temperature something amount water will raise by some other amount now if I want to convert that object into water how much water will be needed so that it will behave exactly like the original object so that much mass of the water which behaves like that object in terms of heat is called as equivalent water amount okay or the water equivalent so it's the mass of water which will accept the same heat for the same temperature as that of the Body for the same Heat and the same temperature got it so forget the body think it has been converted magically into water water and it is behaving thermodynamically heatwise the same way so treat it like water only So eventually we have 180 + 20 which is 200 g of water okay now if you notice what has happened over here who is the cold object cold object is the water over here so 200 g of water which is at 25° C and then the hot object which is the steam the steam which is of how many grams m g m g of steam which is right now at 100° C this is going to lose the Heat and obviously this is going to gain that heat till they achieve what is called called as thermal equilibrium which is happening at 31° so once you identify who gains who loses it becomes an easy problem to solve okay I'll put equal to over here all right water is converting into water because 31° C water is water only so mass of the water 200 specific heat capacity 1 delt T 31 - 25 which is nothing but six so 200 multiplied 6 all right till this point everybody clear right hand side steam directly can't go into water first it has to condense then it has to lower the temperature from 100° Celsius water to 31° Celsius water so it's a two-step process to calculate this first is ml m is M only latent heat is basically 500 140 plus M into specific heat capacity into 100 - 31 is this absolutely clear change in temperature from 100 to 31 and steam to water so m is common I believe so here we have 540 plus 100 minus 31 that's 69 so basically plus 69 over here so from this definitely we will get m m is basically 1 2 0 0 whole thing divided by 540 + 69 okay so that's just going to be 609 I believe so it's close enough to two yes this is going to be close enough to two because this will be 1 12 0 0 divided by 609 1,200 by 600 is approximately 2 or is equal to two so by 609 will be almost two so this mass will be almost 2 G so 2 G of steam was there that's how you solve the questions is this clear happy bong gash chemistry session Surya is going to be there tomorrow I don't know whether you have seen this please see this okay on the channel only it is there yeah complete maths one short revision 16th January 15th January you have complete chemistry one shot Marathon complete maths formula it is at 7 :00 today we are doing this and before this we have done NT favorite questions I have also done you know a big surprise in terms of test series and also for cbsc board students there is a special crash course where even I am there yeah check that out and also the test series just for 3.99 five mock tests for 399 10 mock tests plus ebooks for $4.99 extra 100 rupees that's all D has taken all the physical inorganic organic marathons 99 percentile questions over here namata M has taken the oisan J series for mathematics before this we have done easy kill questions we have done difficult questions most expected high weightage questions please check out every session it has good collection of questions and in every session you will also see there is a PDF yes just open any session up you'll see the session PDF it has all the questions all the questions over there yeah so solve all these mock test you can give this as a practice and then see the Solutions in our Channel okay that's an easy way to complete all these sessions cool all right let's move let's move to the next question ready Warrior pandus ready Warrior pandus wpwp Warrior pandus whistle puu wbwb please I need some energy huh H berol is equation come on let's go yes even today's session PDF will be given in the comments or in the description box the PDF link will be uploaded okay just wait till tomorrow morning it will be done okay great hold on we are coming to ktg hold on burnol is equation pressure plus half r v s plus r g is a constant pressure at any point row is density V is speed r g h g is gravity acceleration H is the height this is the formula which you use for pipes basically or for streamline flow maybe the height here is H1 maybe the height here is H2 maybe the pressure here is P1 pressure here is P2 the velocity here is V1 the velocity over here is vs2 so then you can use this concept from one cross-section to other cross-section something like this P1 plus half density into speed square plus row G height 1 is equal to pressure plus row G H2 plus half row V2 s not just that if you change the cross-section speed changes maybe the area here is A2 area here is A1 so you have something called as equation of continuity which says V1 A1 is equal to V2 A2 and this quantity over here is nothing but the volume which is Flowing per unit time so it's the volume flow rate area into velocity is volume flow rate so volume flowing per unit time inside is volume flowing out per unit time that is what the equation of continuity is is all about then I think I have mentioned it over here too okay no issues then you have this viscosity based questions a lot first is the Newton's law of viscosity where if you have a surface or layer of liquid it is moving with a relative speed DV the actual speed might be V plus DV with respect to the lower layer the speed is DV the lower layer might be moving at a speed V then if there is relative motion between them there will be a drag Force which is the viscous force between the layers and the fluid slide that drag force is given by AA I will put it over here viscosity coefficient relative velocity which is going to be DV over here by DX and this is actually the force per unit area so you have to put a over here EA a DV by DX what is this DX DX is basically the separation between the layers DV by DX that's the formula this is viscosity coefficient this is area this is relative velocity this is separation so then I don't have to put this over here okay that's what you need to remember is that clear everyone till this point this is Newton's law of viscosity now this is for layers but when you have spherical bodies when you have spherical bodies then you have and you have spherical bodies then you have something called as the Stokes slw then you have something called as the stoes slw where you have a sphere moving with speed V radius is R inside a medium then the drag Force the viscous force is given by viscous force is given by 6 pi RV 6 Pi viscosity coefficient into radius into velocity this is your Stokes law my dear students based on that Stokes law you get the concept of terminal velocity for any object which is dropped so maybe the object starts from rest it starts from rest slowly the speed increases and eventually the speed just remains constant so this is your terminal velocity which remains constant and that formula for terminal velocity is given by 2x 9 Okay g into radius squar divided by viscosity coefficient density of the drop or that sphere minus the density of the fluid please remember here this is for the fluid this is for the drop that's something which many students get confused over here okay this is the terminal speed velocity and when the terminal speed is achieved when the terminal speed is achieved you will see that the buyant force which is V Ro G and the drag force and the viscous Force basically which is 6 Pi RV will be balanced by the weight which is M into G so this is what happens when the terminal speed is achieved because they are balanced that's why the acceleration will be zero the acceleration will be zero and the velocity will be constant these concepts are very important for these questions then the toriles law again this is based on Bern's principle if you have a bucket of water like this and maybe it is filled with some liquid over here dis filled with some liquid over here like this till some height let's say the height till which the liquid is filled is H now somebody makes a small hole over here somebody makes a small hole over here at a depth of small H then the velocity of that liquid which is the velocity of f flux is given by root of 2G this H the height from the surface this liquid will definitely fall somewhere this liquid will definitely fall somewhere so you will basically get the range you will get the range that range is given by 4 * H - H into H H is this complete height small H is from the surface this is what the range is going to be this is very very important yeah yes all right now next important thing next important yes uh see all the planes Wings fans everything they all have this concept of pressure difference which is created by velocity difference so they create a differential velocity which creates a differential pressure that pressure difference is what creates that Force that's what happens one part will have slow moving velocity one part will have high moving velocity of liquid that is what creates the pressure difference every time Aeroplane houses flying off during tornadoes uh Blades of a fan or a rotor all these things okay these are the important formulas also the rate of flow the rate of flow of the liquid which is coming out will be the area of that small hole area of that hole multiplied by the velocity the same velocity the velocity of fux very very important sometimes they might also ask you what is the force of that liquid coming out the force of that liquid or basically that F flux that is density into area multiplied by the velocity Square row a v² that's the formula the Velocity in square into the area into density gives you the force with which the liquid comes out through any hole these are the important formulas here so let's start with some questions here it comes a tube spray pump has radius R it has n holes each of radius R speed in the tube is V what is the speed of the liquid through the holes very straightforward question so imagine this is a tube of radius basically let's say R and inside of it the liquid is entering uh with a speed V now what happens is as you go ahead it breaks down into small small tubes n number of such small tubes and each having how much radius small R and each of them the velocity let's say call it as U so n number of such tubes are there so the question is what is that speed I believe what is the speed of ejection of liquid U is asked what is this U so use a uh you know equation of continuity so which says that the rate the rate of liquid going in is the rate of the liquid which is going out now the rate of the liquid which is coming in is area into the velocity area being Pi into r² Pi into r² so into velocity the rate which is going out there are many such tubes many such tubes each tube has a area let's say small a the velocity is U but there are n such tubes so multiplied with n this small area will be Pi r² into U into basically n Pi Pi cancels Pi Pi will cancel definitely therefore U will be check this out U will be R square is there V is there from here R square will go down and even n will go down so r² V by r sare n that is the answer R square V by R square n which is B option everything else there is some or the other thing which is unnecessarily squared or not squared yep cool everyone these are the important important obviously Concepts from fluids which you must must know moving on to the next question there is a liquid going through a horizontal pipe if the pipe is horizontal that means the height is not changing it is constant speed is V where the pressure is p another point pressure is less but the speed is different if the density is row and the flow is streamline then what is capital V going to be okay so for this particular question remember the height is not changing only the pressure and the speeds are changing pressure is p here it is p by2 here it is going with speed V here it is coming out with capital speed V and this capital V is asked so let's use Bern's equation height is constant obviously height is going to be the same so pressure plus row g h + half row v² is equal to here it is p by2 + uh r g h plus half row capital v² r g r g cancels so P minus P by 2 is equal to half row v² or half I'll just keep this small v sare as it is half row small v² is equal to half row capital v² P - p by2 is p by2 so P by 2 + half row v² is equal to half row Capital v² half half half cancels so p+ row small V square is row Capital v² so v² capital V Square Capital will be P by row plus v² so V will be root of P by row plus small v s p by row plus small V squ which is D option I believe yes that is the correct answer got it everyone yes the D option very good nagar come on guys full energy full Jo I want everyone okay awesome awesome awesome let's move let's move to the next question are you already this answer is given anyways try to do this question now homework because already the answer was given okay this is based on the concept pressure difference uh is nothing but that Force which is created per unit area and this pressure difference comes because of the Velocity which is different use barnoli use barnoli principle yeah use the barnoli principle why are all the answers given so [Music] quickly okay try to do this also as homework anyways try to do this also as a homework uh terminal velocity is given Visos it is given speed is also given radius is also given what is the viscous drag Force this is a question based on stoke's law stoes law viscous force is 6 Pi ETA RV believe me everything is given EA is given ITA is given radius is given also speed is given you just have to find this 6 Pi RV directly you can do this question okay let's do the next question luckily answer is not given here okay solid sphere of certain radius acquires some speed through a medium of viscosity it is broken down into 27 small spheres each of this acquire speed V2 what is ratio of the speeds what is the ratio of the speeds okay now for this particular question find the new radius your job will be done because remember the terminal speed given formula is 2x9 G r² Sigma minus row whole thing divided by e so terminal speed is proportional to r² so when I want to do V1 by vs2 it should be R1 by R2 whole Square so what do I do now if you take a big sphere break it down into small small parts the volume which is there of that big sphere will be volume of that small spheres multiplied by the number of such drops multiplied by the number of drops each drop some volume add all those volumes small small small small drops you get the volume of the big sphere what's the volume of the big sphere 4 Pi I think R Cub / 3 4X 3 piun RB is equal to volume of the small one will be 4X 3i R2 Cub number of drops 27 4X 3 Pi cancels so R Cub will be R2 Cub multiplied 27 take cube roots so R will be 3 * R2 rather this R is actually speaking R1 so R1 by R2 R1 by R2 will be 3x 1 makes sense so the new radius is 1/3 of the previous one so R1 by R2 is 3x 1 so this will be 3x 1 whole Square so that's it guys you are going to get this as 9 by 1 so 9 by 1 I believe or 1 by 9 yes with 9 by 1 which is option a yes correct perfect one this is 9 9 by 1 is the same as 9 correct got it guys everyone yes option a Perfecto awesomeness these are standard questions let's go to ktg and Thermo let's directly go to now to ktg and thermodynamics after this ready for it okay cool let's go my dear students boils law when temperature is constant P into V is constant pressure is inversely proportional to volume that is your Bo's law next Char's law when your pressure is constant then your volume is directly proportional to temperature that's your Char's law next your Gus's law which is when your volume is constant then pressure is directly proportional to temperature hence you get PV is equal to nrt which is your complete ideal gas equation PV is equal to nrt n is the number of moles R is your gas constant T is temperature in Kelvin V is volume p is pressure you can also rewrite this formula as PM is equal to row RT where m is the molecular mass m is the molecular mass row is basically the density row is basically the density if you ask me how to calculate the number of moles I will say you can do it like this number of molecules by the avagadro number this is avagadro number 6 into 10 ^ 23 or you can also do mass of that particular gas mass of that particular gas upon the molar mass upon the molar mass that will also do mass of that gas upon the marar mass is that right yeah okay so that will give me the number of moles cool next important formula for RMS speeds and all these things so RMS speed is root of 3 RT bym standard where RMS value means root means Square so it is taking the squares of each speed V1 Square V2 square like that taking the average that means divide by n and then finally taking the root that is your root mean Square speed it's 3 RT by molar mass standard formula which you should know okay then some more formula I will give it to you right over here which you should definitely know you also have something called as the most probable speed and you also have average speed average being V1 + V2 + n molecule divided by n average speed is nothing but three sorry 8 RT by pi M most probable speed is root of 2 RT by molecular mass and you have the main ktg equation of pressure and RMS speeds which is given by pressure into volume is 1 by3 number of molecules mass of each molecule into RMS squ this is number of [Music] molecules this is mass of each molecule mass of each molecule very very important this mass of each molecule is the molar mass divided by avadon very crucial again okay keep this in mind very good awesome now the next thing which you should know is a table chart for monodia par polyatomic gases standard basic results so when you talk about monoatomic gases like example helium neon Etc and then you have diatomic gases uh example hydrogen oxygen or even uh uh triatomic gases but which are linear triom make gases which are basically linear example CO2 and then you have nonlinear nonlinear triatomic triatomic gases example H2O yeah for each of them you have something called as the degrees of freedom the degrees of freedom for monoatomic you have three translational degrees of freedom then for diatomic you have three trans or even for linear three translational plus two rotational degrees of freedom which makes it five degrees of freedom the symbol is f degrees of symbol Freedom the symbol is f nonlinear triatomic you have three translational and three rotational which makes it six degrees of freedom then you have something called as the specific heat capacity at constant volume which has a formula degrees of freedom R by two so for mono like helium neon Etc it is going to be 3 R by2 this is going to be 5 R by 2 you can see degrees of freedom is five this is 6 R by 2 which is going to be 3 R then you have CP which is cv+ R which is mayor's relation so CP for mono will be 5 R by2 for diatomic it will be 7 r by2 and for triatomic nonlinear it will be basically 4 R then you also get something called as gamma which is the ratio of CP by CV gamma which is the ratio of CP by CV which is also 1 + 2x f for monoatomic the gamma will be 5x3 for datomic it will be 7x 5 for nonlinear triatomic it will be 4x3 these are the formulas yes is this clear everyone these are main things that you should know in ktic theory of gases apart from this some more things which you should know is the law of equip partition of energy which says that the energy the energy the energy per degree of Freedom per molecule per molecule is half KT where K is Boldman constant which is R by NA which is 1.38 into 10 ^ minus 23 this is your bold's man constant so keep this in mind the total energy of a molecule the total energy of a molecule is degrees of freedom degrees of freedom into half KT whereas the total energy of a gas is given by number of moles into CV into T So change in internal energy of a gas is n CV delt this is again a formula which you must must know gamma is your adiabatic ratio poison ratio whatever you want to call it okay so CP by CV ratio adiabetic ratio right that is what it is now let's solve some questions based out of this here is the first question there is a graph given of pressure versus temperature all these gases when extrapolated they meet at this particular Point K the question is what is the temperature corresponding to that particular point it's a very simple ladu question everybody should be able to give it gamma is useful for calculating work heat Etc in adiabetic processes it is also useful for calculating you know pressure volume temperature for those processes where heat exchange does not happen basically an isolated system correct so that is where you will see it used it's also useful for calculating the speed of sound which has the formula root gamma RT by m okay speed of sound so many places you will see the usage of gamma yes this has to be absolute zero which is - 273° c perfect very good awesome yes option A next the RMS speed of oxygen is 160 RMS speed of hydrogen at zero is how much now remember RMS velocity is < tk3 RT by m temperature is same so it is indirectly proportional to the root of the M Mass so that's all so velocity of hydrogen by velocity of oxygen will be M Mass oxygen on the top Mar Mass hydrogen below so what is for oxygen well it's 3 for hydrogen well it is two so it will be root of 16 which is basically four so velocity of hydrogen will be four * velocity of oxygen so 4 * of 160 16 4 are 64 so 640 m m/ second 640 is option A yes it is correct simple formula indirectly proportional to root of mass and that's what will give me is that clear everyone moving on next question on your screen diatomic gas does 100 Jews of work in isobaric expansion what is the heat given to the gas all right let's do this diatomic gas is doing 100 jewles of work okay work is known in isobaric expansion that means pressure is constant so usually the formula for work is p Delta V and this is given to be 100 100 is basically P Delta V okay what have we been asked the heat given heat for isobaric process will be n CP specific heat capacity at constant pressure delta T from diatomic gas diatomic gas CP value we just f f it out in this table remember diatomic gas CP value is 7 R by all right so let me just put it over here diatomic gas it will be nothing but 7 R by 2 and this is nothing but delta T now you'll be like how do I find this this is given I have an idea let me write this as 7x2 NR delt T you know what NR delt is nrt is PV so NR delt T is p Delta V yes PV is nrt so P Delta V is NR Delta that's a differentiation on both sides derivative difference on both sides that's all so P Delta V is 100 so just put 100 over here so that into 7 by 2 100 by 2 is 50 57 is 350 Jew so that is the heat option number c this particular thing is useful many many times so I will just mark it here p P into V is nrt so P Delta V is NR delta T assuming the pressure is going to be constant n and R are always going to be constant so that is a very very important relationship which you must know which we have used it over here okay cool let's move to the next question how much energy do 10 non- rigid energy uh non- rigid molecules have at some temperature t h 10 10 non- rigid molecules diatomic molecules I think I know energy of each molecule energy of each molecule is half KT into degrees of freedom so half K is also there t is also there diatomic has 5 degrees of freedom so for 10 molecules for 10 molecules the energy will be 10 * 5x 2 KT correct 10 by 2 is 5 55 are 25 so 25 KT 25 KT I think they have missed something why have they written 35 KT 10 non-rigid diatomic molecules diatomic molecules have five degrees of freedom yes perfect Perfect k is K only T is T only there are 10 molecules 10 by 2 is 5 5 5 is are 25 I think it's a misprint it shouldn't be 35 uh unless unless we consider vibrational degrees of freedom so I think either you give in the question that also considering considering vibrational degrees vibrational degrees if you consider vibrational vibrational degrees the degrees of freedom will be added by plus two so then over here what will happen is over here this won't be five this will be basically 5 + 2 which is going to be 7 so three translational two rotational and two vibrational modes will come so because of which it will become 7 so half KT into 7 yes perfect so then 7x 2 KT will be multiplied by 10 so 10 by 2 is 5 5 7 35 so 35 KT will be there considering vibrational modes and this will only happen when the temperature is very high not at normal temperature normal temperature vibrational degrees are not there only at very high degrees at very high temperature it will be there okay I hope this is absolutely clear and I think uh the hint can also come from this part over here where they have mentioned that it is non rigid non- rigid means the distance between the molecules can change so definitely they can vibrate so that is the reason why we should actually consider the vibrational degrees of freedom so technically speaking this question is fine only no need of mentioning this because non rigid is mentioned that means the molecules can go back and forth with respect to each other so vibrational modes have to be considered okay so this happens at high temperatures usually and uh you have to add extra two degrees of freedom all right next beats resonance coming towards the end of the 11th part yep yes Ashwin non- rigid is given very good clear is this question pyq I'm not really sure some questions might be pyq some are not and these days there are so many pyqs because there are so many shifts no so many shifts so many attempts some years there are four attempts three attempts so the number of questions are like crazy so it's very difficult to remember these days which is a pyq non pyq J Advan question at least you can remember it means questions it's like when it's like piece of garbage like garbage is thrown everywhere so much so many questions are there just have to solve pyqs okay beat frequency beats is when two sounds of similar wavelength similar frequency Al together individually they sound the same but when sounded together they will alternatively produce loud sound faint sound loud sound fade sound so that loudness and faintness leads to that phenomena of Beats and there is a rate at which that loud faint loud faint goes on that is called as the beat frequency that is precisely the difference of the frequencies whichever is Big put it first whichever is small put it later on cool yeah awesome yes when will the class complete the target is to complete it by 6:00 hopefully if it doesn't maximum 6:30 okay because 7:00 you have the mathematics class all right now whenever resonance occurs okay then remember two things will vibrate with maximum amplitude their frequencies will be similar to each other so whenever the word resonance is used frequencies are same amplitude is maximum sound light whatever it is it is maximum when they are identical but not equal they will produce beats the difference of the frequencies when you load a tuning fork with wax or some material some clay then the tuning fork becomes heavy it becomes slower and the frequency reduces keep that in mind now the most important uh repeated question in these is about pipes organ pipes and this resonance tube specifically you should remember one thing when you have a completely closed or complet completely open on both sides a pipe which is open on both or closed on both sides the frequency is given by n * velocity of sound by two * of length this is the length of the pipe speed of sound n is the harmonic number so you have all the harmonics f is there 2f is there 3F is there 4f is there 5f is there and so on and so forth this is called as the fundamental frequency this is called as the fundamental frequency but if it is open or closed on one side only such an organ pipe such an organ pipe will have a Formula F is equal to odd V by 4 L be careful two here four here the frequencies of such pipe will be F 3F 5f basically 7f odd F odd harmonics only even are not present this most basic is again called as fundamental frequency this is third harmonic fifth harmonic seventh harmonic ninth harmonic even harmonics are absent Now using the concept of open closed end you take a pipe dip it in water so this side becomes closed and this side becomes basically open pipe you take a fork of frequency F sounded the standing waves are produced inside this particular pipe open and closed and the formula for frequency is given by odd times V by 4 L but this length is the effective length because there is something called as the end correction which is the original length plus plus3 * the Dieter this is called as the end correction this end correction is because your standing waves do not exactly end on the open side they go slightly outside of the open pipe so you have to accommodate that extra length which is called as the end correction e so the length that you put in this formula should be the geometrical length plus some additional factor which is3 * D where the D is basically the diameter of that pipe diameter of that pipe that's all now when you vary the length when you can make this pipe go up and down you can get different harmonics the first harmonic when you get you will see there is an antinode here node here and you will see that the total length of the pipe plus the end correction will be Lambda by 4 this is the first harmonic that you will get then in the second harmonic next harmonic anti node node anti node node so you will see that the length plus the end correction this this will be the next length will be you know this is Lambda by 4 this is Lambda by 4 Lambda by 4 Lambda by 4 so this will be 3 * Lambda by 4 next time when you change the length of course okay so this will be the next length I can call it L3 this will be let's say L1 okay the wavelength will also change uh if tuning fork is different if it is the same wavelength will be same this will be obviously the third harmonic same thing you can go for the next one also so it will be basically L L5 plus e will be 5 * Lambda by 4 this is going to be the fifth harmonic so as you move the pipe up and down more and more wavelengths will fit in and accordingly this lens will change as per these formul remember how do I know this Lambda by 4 because if I have a standing wave this particular lobe which is there this is actually Lambda by 2 and how do I know it is Lambda by2 because look at this this is completely one wavelength this is a wave so this is half the wavelength so if somebody only considers this much only considers this much that much will be Lambda by4 and in fact this is exactly what is considered here anti node node it's half of the lobe half of the lobe Lambda by 2 is half is Lambda by 4 that's why I have taken this as Lambda by4 okay so keep these things in mind no problem puos welcome aboard yes thank you so much mutul lakmi means a lot yes whole of the physics portion all the high weightage topics yeah cool let's do some questions oops based on this uh yeah a resonance tube is old and has some uh you know some weird end Jagged end means it is not very great it is still used in the laboratory a tuning fork is used and when the tube is filled with water uh to a mark of 11 cm then the open end of the tube then there is a resonance the experiment is repeated with another fork and the mark is 27 CM so the velocity of the sound in air obtained in this experiment is approximately how much come on let's see how do we do this particular question very interesting the first resonance then uh you know the experiment yeah produces the first resonance first resonance means the first harmonic this is the original Len there is some Jagged end means there is an end correction involved here okay keep this in mind so length + e is equal to nothing but that odd number into Lambda by 4 in this case is the first harmonic so odd number is one this is Lambda by 4 length of the pipe is 11 cm so11 M plus the end correction this is the first equation similarly in the second case it is repeated with a different tuning fork okay different uning Fork so 512 and 256 so think about it if this gives some wavelength frequency is haved what will happen to the wavelength frequency frequency is half so what will happen to the wavelength the wavelength will become two * Lambda if this was Lambda that will become 2 Lambda yes or no everyone clear till this point okay so next time what is the length 27 CM so I can say next time Point 27 plus the same end correction again the first resonance that means first harmonic that means odd number is one that is 2 Lambda divided 4 that is number two obviously e is not known from this I can find the Lambda and then solve for the question that's all so subtract the two guys nothing great over here take this and subtract the two subtracting you will get 27-11 e will get cancelled 2 Lambda by 4 2 Lambda by 4 minus Lambda by 4 this will be nothing but6 is equal to just Lambda by 4 so Lambda will be oops Lambda by 4 so Lambda will be 4 * .16 which is 64 M now you can find the speed of sound so speed of sound will be f * of Lambda f is 512 and Lambda is nothing but 64 so do the math and you will get the answer as 328 m/s so this will be nothing but 328 m per second is this clear how to solve this question yep awesome awesome very good clear let's move to the next question on your screen there is a tube both ends open tube one end closed otherwise they are identical the ratio of fundamental frequency of tube a and Tube B okay simple guys if you take tube a has both ends open the fundamental frequency of tube a will be n v by 2 if you take tube B one end is closed the fundamental frequency will be odd V by 4 L what is the ratio of the fundamental frequency if they are identical in nature okay just take the ratio guys F A by FB V by 2 L V by 4 L so it will be 4X 2 which is 2 is 1 so 2 is to 1 which means option number c yes correct option C which is 2 is 1 very good let's let's go to the next question a closed pipe gives seven beats with an open pipe both in the fundamental mode what is the speed of sound very nice question let's try to solve this if you take a closed pipe if you take a closed pipe which produces with an open Organ Pipe now closed means it is closed on one side don't take it closed on both sides so if it is closed on one side the formula for the frequency will be odd V by 4 into the length length is 150 CM which means 1.5 M next thing open Organ Pipe that means it is open on both sides length is 350 so for that guy n v by 2 into length length is 3.5 M okay so this will be nothing but V by 7 this will be nothing but uh V by 6 obviously V by 6 is more as compared to V by 7 it is clearly mentioned in the question 7 beats per second when both of them are together so fub1 minus FS2 is 7 so therefore V by 6 - V by 7 is 7 take the LCM so 7 V - 6 V by 6 into 7 is equal to 7 is that right okay right okay so this will be nothing but v ided 6 * 7 is equal to 7 so V is equal 7 into 6 * 7 how much is this velocity how much is this velocity come on my dear Warriors 7 7 are 49 into 6 well 50 into 6 is 300 100 so take out six from it so it will be 294 so 294 m/ second just check this out okay yes the answer is 294 perfect the answer is 294 very good awesomeness oh it's break time because now after this we have 12th standard syllabus I think 12 standard syllabus not many topics are there okay because 12th syllabus is much lesser than the 11th syllabus so we'll be able to do it on time hopefully okay so we'll take a break quickly and then we will start with the 12th standard syllabus okay we'll take a 10 minute break guys e e e e e e e e e e e e e e e e e e e e e e e e welcome back welcome back everyone wow what a session it has been and we started at 11:00 in the morning it's going to be almost 6 hours are you guys all ready J Advance is already ready to blast J Mains somebody's from Kor tanor wow hi welcome back awesome welcome welcome welcome aboard everyone yeah perfect disaster ready Padu 29 shift wow uh you will get enough time nikil from Andra hi STI yes your capto is back yeah very good session thank you so much P ready shat shiv welcome let's go now starting off with kum's law based questions kum's law in electrostatics which is K q1 Q2 by r² charges product divided by the distance Square K is the Kum constant which is 9 into 10^ 9 which is having the Formula 1 by 4 Pi Epsilon not which is permitivity which is having the value of 8.85 into 10 the power basically ne12 now usually this permitivity can also change the permitivity of any medium is permitivity of free space into K this K is not the same as this K over here this is your dialectric constant a dialectric constant of that particular medium usually it will be like 2 3 4 100 whatever some value will be given because of which the force can become less the electric field intensity can become less when you place these same charges in a different medium so the choice of medium decides the you know quality of the electric field and the electric force that's a very common thing in electrostatics is that right okay so let's do some questions based on the electrostatic force and all of that and by the way this force is also going to oby superp position principle and standard things so the net force will be F1 plus FS2 like that till the nth Force you can do this you can also find the field due to this and the field due to this particular force will be electric force divided by the charge electric force divided by the charge that is the electric field value how much force is there per Kum of charge per Kum of charge let's do some questions this was asked in J 2024 in a hydrogen like system the ratio of Kum force and gravitational force between two electron between an electron and a proton is how much approximately so if you take an electron and you take a proton obviously the masses are also going to be different but what is the ratio of the electric force upon the uh gravitational force the electric force will be K q1 Q2 divided by r² whereas the gravitational force will be g m m / r² now obviously the question demands us to take the ratio of this so the electric force divided by the gravitational force will be K by G here you will have e s here you'll have mass into mass now these values you can substitute and get it K is 9 into 10^ 9 G is 6.67 into 10^ - 11 electron charge is of the order 1.6 10 ^ -9 mass of uh uh mass of what is this electron is 9 into 10^ -31 mass of a proton is close to 1.6 into 10^ minus 27 these are approximate values you can just substitute it and the value that you will get is 10^ 39 best is to remember this value because many times these questions come in different exams State entrance bits so many places so remember it is 10 the^ 39 times stronger so electric force is very very strong as compared to the gravitational force is that right everyone okay cool moving on to the next question on your screen this was also asked in j24 the force between two charges in vacuum is f when you place a dialectric medium at r by5 distance what's the new Force going to be so if you ask me what's the old Force formula for the distance R it will be kums constant into q1 Q2 / r² now when we find that new force that Kum constant will now become divided by five and the charges are still the same the distance is R by 5 so this will be R by 5 whole Square so 5 five will cancel K q1 Q2 ided r² by 5 one of the fives got cancelled so five will get multiplied in the numerator else you will have K q1 Q2 ided r² this is same as this so it will be that Force multiplied by five so the new force is five times the old force that is the answer which is option A I believe right perfect whenever you have the dialectric medium constant given always divide the older Force by that dialectric constant because the force always becomes lesser as compared to previous it becomes weaker okay I hope this is clear ramasar which part of the previous question you did not understand please let me know this is electric force charge on electron charge on proton K q1 Q2 by r² gravity gra itational Force G M1 M2 by r² when you divide both of them R sare R square will get cancelled out so this is what you will get K by g e s by mm correct constant this gravitational constant is this electron charge is this value mass of an electron you should remember this mass of a proton is 10 the^ -27 if you remember these values it will be easier else you cannot do this question unless you already know this value somehow okay fine okay next question coming up on your screen is on electric Fields different formulas if you have electric field to be found for different things all the formulas are given here remember electric field is force per unit charge starting off with due to a ring if you have a Charged ring on the axis of it the form is k q into the distance divid r² + distance Square raed to 3x2 on the axis of the Ring similarly if you have electric field due to a large sheet the sheet will have a charge density Sigma the formula is Sigma by 2 Epsilon Sigma by 2 Epsilon it is a uniform field on both the sides keep this in mind this was for the ring and here this Zed represents how far you are and this is the radius of the ring so at this point how much electric field will be there here uh in this particular thing you have a Charged sheet the electric field will be here also and here also how much electric field will be there is given by Sigma by 2 Epsilon KN okay this is a charged sheet remember that okay similarly due to a thin shell shell means it is like this this is the radius R the charge is distributed only on the surface or it's a conducting sphere so charges are only on the surface if you're inside there is no field if you're outside it behaves like a point charge so you just measure the distance from the center it will be KQ by r² if it is a shell if it is a solid sphere uniformly charged meaning just visualize as if every everywhere even inside of it there are charges everywhere scattered okay uniformly then this is the radius if you are outside then as if all the charges concentrated here measure the electric field so KQ by r² but if you are inside then it is KQ by R CU into R so it is proportional to R remember that in fact the graphs are also very critical over here if you draw the graph of electric field with distance that graph will be straight line and then it will go like this whereas for here if you draw the graph of electric field versus distance it will be zero it will suddenly climb up and then it will go down so that's how the graph looks like for a shell if you remember the graphs also often you will immediately recollect oh it was a straight line so it is proportional to R so to compensate the dimension you will make it R Cube below R Cube below okay I hope this is clear all right should we memorize all yes you have to memorize all correct there is no other option okay moving on to the questions infinitely Long Hollow conducting cylinder with the radius R carries oh I why magnetic field question came over here by mistake no issues um by mistake magnetic field question has come anyways still we can do it it's not like we should not do it uh anyways so if you have this is not a question on electrostatics guys this is a question on magnetic field if the current is going only on the surface only on the surface of that particular cylinder okay so question is what is the magnetic field around it going to be what is the magnetic field around it inside what will happen there will be no magnetic field inside the magnetic field is zero in fact this cylinder behav behavior is very similar to this behavior of a shell inside the shell there is no field only outside there is so the behavior is very similar so inside it will be zero so a c and b graphs will go away so as you can see inside it should be zero and once you go outside the formula for magnetic field is Mu I by 2 pi r so it is inversely proportional to R outside so as you can see it is inversely proportional to R right over here so it should be basically D option yes it is a d option okay this question shouldn't haveen here but it's okay I mean we all know magnetic field formula and all of that is that okay everyone let's move to the next question a particle is moving along a circle of radius R along an infinitely long wire yes that reminds me there was one more formula which was missed over here so let me just add it if you have a wire which is like this and you are standing at a distance R from here and you want to find what is the electric field the electric field will have two components ex and ey this is a linear charge distribution some charges are there over here uniformly distributed and that charge distribution is Lambda which is the charge per unit length Lambda then all you need to do is draw a line from here to here here to here call this Alpha call this beta this ex will be 1 by 4 Pi Epsilon Lambda by R here it will be sin of alpha plus sin of beta whereas ey the Y component will be again 1X 4 Pi Epsilon Lambda by R here it will be cos Alpha minus cos beta from this you get if it is an infinitely long wire if it is an infinitely long wire then Alpha and beta both are 90° and the electric field will come out to be 1 by 2 pi Epsilon Lambda by R this is the value that you'll get for an infinitely long wire instead of four you will get two because when you put 90 90 sin 90 sin 90 1 + 1 will become two two will cancel with four it will become 2 pi Epsilon that's for an infinitely long W I think this question is based exactly on that a a particle is moving in a circle along an infinitely long wire which is charged of density Lambda what's the time period going to be K is the kums constant so think of a very long wire think of a very long wire this has positive charge on it and a particle of charge minus Q so that means negatively charged particle will get definitely attracted towards it and this is going in a circular path like this whose radius is basically R whose radius is basically R so that will experience an electric force here that will cause centripetal acceleration like this it will have some velocity over here and uh or rather I will say it will have some angular velocity like this so I can say by Newton's law the centripetal force is mass into centripetal acceleration this force will be electric field into the charge acceleration is Omega square into R electric field due to an infinitely long wire is 1x 2 pi Epsilon Lambda by r q is is here M Omega s r is here so bring R and M on this side 1 by 2 pi Epsilon I can write it as 2x 4 Pi Epsilon into Lambda by r² and M is also going to be here Q is going to be on the top this is Omega Square what is this this is 2 into K 1 by 4 Pi Epsilon is K kums constant Lambda Q divided by r² m is equal to Omega Square from this I will get Omega which is the root of all these things so the root of 2 K Lambda q ided r² m but Omega is 2 pi by time period Omega is nothing but 2 Pi / time period and we want the time period so time period will be 2 pi under root time period will be 2 pi under root r² m / 2 K Lambda q that is what it will be if you want take R outside also that is okay so that is going to be D option I believe yes perfect D option is correct 2 K Lambda q m is there R can be taken out so it will become 2 pi r is that right yes we can do it by Dimension but it might be little bit difficult at times to go by Dimensions because these are all weird weird things kums constant has some unit and all of that next let's go to the next question huh capacitance capacitance of a device any device which can store charge and it will store energy between those two conductors is called as a capacitor it will basically store charge and electrical energy between those conducting plates and the charge stored on a capacitor is given by capacitance into the voltage difference between those two plates or conductors capacitance is measured in farads if charges in kums and plate voltages differences is volts now if you have a parallel plate capacitor the formula is Epsilon a area of the plate divided by the distance of the plates if you add some dialectric medium over there then you can multiply this with K which is the dialectric constant which is the dialectric constant of that this is one major formula which you should know now when you store that energy how much is that energy that is given by half CV square or Q sare by 2 C or half QV all formulas are the same because Q is CV that formula if you use and substitute it here you will get any of these combinations there is also a formula over here for electrical energy density electrical energy density which is given by half half permitivity into electric field Square so this is the energy density energy per unit volume is half Epsilon e s is the electric field this is also seen in this particular chapter if you combine capacitors in series use the resistors in parallel formula if capacitors are in parallel then use capacitors in sorry resistors in parallel sorry resistors in series formula it's exactly opposite of resistors when capacitors are in series it is the charge which is going to be the same and it is the total voltage which will be V1 + vs2 + VN in parallel the voltage will be the same and the total charge will be q1 + Q2 like that for all the in capacitors is that right this is what is going to be any method that you know for finding equivalent resistance be W Stone be disguised form bit uh bridge wones bridge or any series parallel combination trick that you have learned all the things kovs laws are still valid for capacitors are still valid for capacitors also the standard most problem if you take a battery of voltage e take this switch and take this capacitor and charge it if the energy stored in the capacitor is half c² then the work done by the battery will be C Square so you might be wondering if battery did C Square work energy stored is half C Square where did the other half of C Square go it will go in basically heat loss so when you charge a battery by closing the switch you will see half of the work done by the battery only gets stored and the other half is going to get lost in the wires resistances this is also uh very very important all right oh my God who is this okay don't worry this I'll ask uh the moderator yeah don't worry the moderator will block them yes so make sure guys please don't spam like this it is uh not great I mean other people are studying here seriously don't spam over here unless you really have something to ask Will you post this video what do you mean by will I post this video this video is already live no what do you mean by that who told you 28 29 shifts are tough who are these people who are telling you all these things 28 29 will be tough 2425 will be easy based on the past year Trends guys please stop watching all such videos I mean really what no nobody will nobody will be able to guess such things okay so don't waste your time chuma that 24th will be easy because it is a first day they don't want to scare you what they n people are doing some favor on You by keeping the paper easy on the first day because you will be shocked do you think they really think so much no nobody thinks so much guys yeah so please don't waste your time so much they will not do this kind of analysis oh the last day people would have seen all all the shifts so they know all the questions so I have to make a different question paper set and it has to not match with any other the model papers it has to be way tougher students will think it will be easy so we'll make it tough think these kind of Mind Games they have really time they can't manage so many things properly oh my God yeah many YouTube De and Bas only basically de and bayas correct you are right because first of all they would not have even gone into that graduation mode they would not have complet their graduation and before graduation only you start making these videos I mean you should be teaching in that J batch for at least two years one year at least one year two years you should have taught then you will know that all these things you will never say okay let's move figure shows charge versus voltage for the two given capacitors the capacitances are what okay so charge versus voltage is given and we know Q is equal to C into V so C is equal to Q divided voltage so if you talk about the first capacitor which is a so the capacitance a will be charged by voltage so I can take the voltage as 10 charge is basically 500 micro voltage is 10 so it will be 50 microad so so 50 microfarad is only there in one option as you can see in C option you don't even have to do the other thing but on the safety side if I want to find capacitance B charge will still be how much 80 so 80 micro divided by 10 which is basically 8 microfarad so that is option C of course Very straightforward moving on to the next question believe me this question came in j29 yeah there you go thank you all right what is oops sorry why the slide goes off eight drops combine the capacitance is how much now this kind of questions no they are based on this concept where if you have a sphere this is an isolated spherical isolated spherical capacitor if the radius is R then the capacitance is given by 4 Pi epsilonr just like you have parallel plate capacitor this is spherical capacitor that's all now if you are going to combine eight drops into one big drop so the volume will be conserved so 8 times volume of that small drop will be the volume of that big drop over here so 8 * of 4x3 < R Cub is 4X 3 Pi capital r which means 4 by 3 Pi cancels so 8 small R Cub is capital r Cube taking cube root 2 R is equal to R so the radius has been doubled so think about it logically if radius is made two times the capacitance will also be made two times so hence the answer will be two times very straightforward okay very good anandu disaster where am I from right now I'm in Bangalore but I was born in Salem I have did most of my education in Pune Mumbai nagpur yeah that's how it is okay moving on to the next question on your screen two capacitors are charged and they charged with different voltages then they are connected in parallel the positive is connected to the negative oh my God the final energy is yes these kind of questions are also going to be very very common oh you are also from Salem SES welcome nice to see many people from Salam high five yes born tamilan born a tamon being um working as doing service from Karnataka as a canadi uh my education from Maharashtra and uh obviously all my uncles and everyone being Ians yes most of my family is from IIT uh either I Bombay I kpur and all of that so many of my family members and majority of them are from Andra they were born and raised there in Andra so I'm really proud to be a South Indian and uh doing this work for all the South Indians out here who want to learn in English because nobody understands all of us better than us and we know the importance of you know having dedicated classes in English and the importance of U you know learning in our local languages also at the same time and uh having the best teachers not any random teachers yeah uh if I was born in Tamil Nadu I can't be born in Kerala but I wish uh maybe next next life in Kerala right okay so how do you do this question uh we have two capacitors this capacitor is with voltage V so the charge on it will be CV another capacitor 2 C is charged with voltage 2v so the charge on it will be 2C into 2v which is 4 CV now what you do you take take this capacitor positive negative connect it not yet connected now but it will be connected slowly to another capacitor 2C this is negative this is positive so when you do that connection here is the magic which happens by the way these two capacitors together will behave like one single capacitor this will behave like one single capacitor of equivalent capacitance how much they are capacitors in parallel so capacitors in parallel so C + 2 C which is basically 3 C is that right they are capacitors in parallel voltages will be same eventually eventually you know they will have some charge stored on them and this can be converted into one single capacitor which is C parallel this is C this is 2C okay so how much will be the charge stored on them how much will be the charge stored on them that will be because the positive is connected to the negative positive is connected to the negative it will be nothing but 4 CV minus CV why this minus because the positive charge will cancel with the negative charge the positive charge will cancel with the negative charge that is the reason why it should be minus if positive connected to positive the charges will add but positive charge and a negative charge think about it actually it is addition only but you are adding the negative charge think of it like this so hence it will become three times of CV is the new charge parallel capacitance is 3 C question is what is the final energy of the configuration so my dear Warriors the final energy will be half q ² by C parallel q q is basically 3 CV so 9 c² v² C parallel is nothing but 3 C okay 9 by 3 is 3 2 S 2 CC cancels and V Square so 3x 2 CV Square which is D for it Delhi very good we got the answer is that right awesome thank you for all the love Rahul but from Kashmir thank you so much all right wow and I'm pretty sure some of you are already asking the weather I can't even imagine how it must be in Kashmir right now we are freezing out here even in bangaluru because there is a cold wave going on but yeah I'm pretty sure it must be lovely with all the snow uh to look at and doing all the snow activities and experiencing the snowfall the Frozen D Lake and whatnot yeah and gulmar and sonar must be beautiful too with looking at the beautiful rivers with fresh water uh flowing through those uh Scenic mountains must be amazing must be such a picturesque view isn't it moving to the next question what is it there are parallel plates one in front of the other with different distances between them stair like structure who thinks of such things and the capacitance of the arrangement is how much okay now now yeah yeah we will complete the syllabus good boy like a good boy we will complete it don't worry so how do we do this there are multiple capacitors like you can see this is one capacitor then this is one capacitor then this is one capacitor here the area is a the distance is h h h h h so it is basically 5 H is that distance here h h h 3 H is that distance and here it is just H is that right so they are all in parallel because the potential differences are same so so think as if they are all in parallel so C parallel will be C1 + C2 + C3 the first capacitance if you talk about it it will be having a capacitance of Epsilon a by distance which is H the next capacitor which we have will be having Epsilon a by basically 3 H the last capacitance will be Epson area by basically five times of H so this is all going to be like LCM so this will be basically 15 * of H you'll also have Epsilon a common H will go here 15 times here five times and here three times 15 + 5 25 + 3 23 so 23 Epsilon a divided 15 * of H so whatever that is 23 yeah answer is 23 very simple guys do you understand why they are in parallel because this this and this are connected side by side they're all connected by the same wire so potential difference here here and here will be the same got it why they are in parallel everyone yep very good sir will the return Solutions be on the notebook you want me the uh to give the handwritten Solutions also in the PDF no worries I'll give you that okay so the PDF I'll give you the same annotated PDF so that it will be easier for you to revise let's come to loss yes 6 hours now yes I know 6 hours already done wow that is crazy yeah Mery Grace all right so kiro's law first kiro's law is based on the conservation of charge which says that whatever current comes in at a junction is the total current coming out simple next law is based on conservation of energy which says that if you go around a loop and you keep adding the voltages across all the devices the total voltage sum will be zero because somewhere the voltage will drop somewhere the voltage will rise but when you come back the net voltage drop will be zero remember the voltage drop across the battery will either be plus or minus E the voltage drop across a resistor will be plus or minus IR the voltage drop across the capacitor will be nothing but plus or minus uh Q is CV so Q by C the voltage drop across an inductor will be plus or minus L di by DT so these are the main things which you should remember for voltage drops or voltage increases now whether to take plus or minus that is very obvious like if you're going from negative terminal to positive terminal in the circuit of a battery you're obviously increasing the voltage so plus e opposite will be negative current when it flows through the the resistor it will always drop the voltage so in the direction of current the voltage drops against it will increase capacitor is very obvious because positive and negative plates if you assume it positive negative from positive to negative it will drop negative to positive you will climb so it will be plus 10 so that is how the sign convention is for this and remember show the starting point so that you know where to stop or else you'll keep on going around and stop somewhere else so please mark the point when you are using kof's law this is by far the easiest of it so I think we have some questions on this yep we do have so my dear students the question is as follows the question is basically two batteries of EMF 4vt and 8vt with internal resistances 1 ohm and 2 ohm are connected in a circuit with a resistance of 9 ohm as shown the current and the potential difference between the points p and Q is how much voltage difference between the points p and Q do you see both these batter are in opposite directions okay so let's say we start from point q and go around the circuit and come back to that particular point or we can even go like that no issues so let's assume the current to be like this we start from point Q the current is like this the current is coming like this so start from here first time the device you encounter is a resistor you are going in the direction of the current so the voltage will drop how much minus I into r r is 2 next battery negative to positive so it will increase by 8 volts next another battery positive to negative so it will drop by four volts next what is it this particular 1 ohm resistance this particular 1 ohm resistance you are going in the direction of the resistance so minus I into 1 and again 9 ohm resistance so - I into 9 and you come back to the same point so that is basically 0er 8 - 4 is 4 uh - i - 9 i - 10 i - 2 I so it will become -2 I is equal to 0 so 12 I is equal 4 so I is equal to 1x 3 amp that's it this job is done so current is done now the question is what is the voltage difference between points p and Q the voltage difference between those two points p and Q won't it be the same as between this point and this point won't it be the same as between this point and this point so it will be the voltage difference between R so which is nothing but I into resistance current is 1x3 resistance is 9 ohm so it will be basically 3 volts yes it will be basically 3 volts which is the correct answer 3 volts and 1X 3 amp got it my dear students how we do this question very nice perfect let's move to the next question then for the given Arrangement what is the value of the current what is the value after uh uh applying the K's LW all right uh deu we'll try to put the time Stamps no issues okay on 21 this video which is seen by 2x speed is your video I mean what do you mean by that yes this video is good enough to revise most of the syllabus why not I mean I'm covering all the topics which are important and so many topics are there close enough to 100 con Concepts I think we would have done today yeah 100 Concepts is like great I mean there are hardly 25 30 chapters and each chapter we are doing some three four topics subtopics in that so it's a big thing just imagine on an average we are doing three to four subtopics or concepts from every single chapter on an average that's a big big revision Milestone guys what is the current I over here okay so this is 5 ampers this is 2 ampers so at this Junction if 2 ampers goes here this will be 3 ampers so at this Junction five and three will make it 8 Amp 1 and four at this Junction will make it 5 amp at this Junction 8 and five will make it 13 amp at this Junction out of 133 goes here so this will be 10 amp is that right just check this out did we do any mistake over here 5 2 3 yes 5 is 3 + 2 3 comes here five comes here 3 + 5 is basically 8 correct 1 here four here will make it 5 ampers five from here eight from here that will make it 13 out of 13 three goes here obviously 10 will be remaining here none of the options are matching over here so let me just erase this it won't be six yes it will be 10 ampers just check this out everyone confirm done yeah if you do all these Concepts 99 percentile Paka yeah okay cool very good very good very good okay everything fine guys over here just check this out this is 5 ampers here not unless that 5 ampers was on the top then it is a different story alog together okay this five will go into two and three correct this three and this five together will make it eight 1 and four will make it five correct and five and 8 will make it 13 13 will get divided into two unless unless unless this five was on the top then the whole story will change then the whole story will change then what will happen is then what will happen is if assume that this was 5 amp then this thing over here will be 4 ampers as per this Junction because 1 Amper is going here out of two out of four two is going so this will be 2 ampers 2 and five will make it 7 ampers here 1 and four will make it 5 ampers here 5 amp here five and seven will make it 12 ampers here out of 12 three is going so this will become then 9 amp over here so that will be a completely different thing okay I hope this is absolutely clear depending on what the question is so moving on to the next question coming up on your screen here it is resistors having values R1 R2 R3 ratio of I3 by i1 I3 by i1 is how much I3 by i1 is how much okay interesting question so what I can do is over here these two resistors are in parallel and at this point I can apply kof's current law so i1 will be I2 plus I3 using kiro's current law in this particular Loop in this particular Loop if I apply kiro's voltage law what I will get is negative I2 R2 plus because I'm going against the direction of the current plus I3 r 3 is zero so therefore I2 R2 will be I3 R3 so therefore uh what do we have we have to find I3 by okay so let's say I2 by I3 I2 by I3 will be R3 by R2 okay that is what I will get now I2 + I3 is i1 okay so let's apply component property so I2 + I3 / I3 will be R3 + R2 / R2 I have applied compono property compono property which you have studied in mathematics basic maths wherever you have studied it so what will this become I2 + I3 I2 + I3 is nothing but i1 I just wrote it here so this is basically i1 so this whole thing divided by I3 i1 divided i3 because i1 is I2 + I3 perfect is equal to R2 + R3 whole thing divided by R R2 + R3 whole thing divided by R2 so the question is I3 by i1 the question was I3 by i1 so it will be R2 ided R2 + R3 which is B option okay the inverted ratio so therefore I3 by i1 will be R2 / R2 + R3 which is obviously this option perfect kiro's current law kiro's voltage law to the rescue meter Bridge based on the weedston meter Bridge concept meter Bridge based on the wheatstone's balancing concept is nothing but where R1 by R2 is equal to R3 by R4 which can be also written down as balancing length by 100 minus the balancing length here the resistances are as follows 55 by R left by right is left by right left side length is 20 cm so it will be right side length will be 100 - 20 so R will be nothing but 55 into 100 - 20 is 80 whole thing divided by 20 20 goes with 80 four times 55 into 4 is 220 ohms so hence the answer should be 220 perfect very good many of you got it yeah because everybody loves this kind of questions isn't it very nice awesomeness shall we go to the next question current electricity has the maximum weightage keep this in mind moving on the reading of the ideal voltmeter ideal voltmeter means it will not take in any current so ignore forget that there is is a voltmeter just imagine only this much circuit is there and the question is what is the voltage between this point and this point so I think we have to look at only the outer circuit only just look at the outer circuit and then you will realize if the current in the outer circuit is I and you go around it once okay you just go around it once you can apply K's law let's say Start From Here kiro's voltage law start from here the current will cause a difference of minus I into 20 here positive to negative so Min - 4 here again drop of minus I multiplied by 10 here it's an increase of + 10 and you are back to point a so that's why zero - 4 + 10 so 10 - 4 is 6 10 and 20 will make it 30 I is 0o so 30 I is 6 or I is basically 6X 30 which is 1x 5 of an ampere once I get this I can find the voltage shown by the voltmeter that will be voltage between points A and N that will be start from here let's say so there is a drop of minus current into 20 then there is a drop of 4 volts over here just take the mod value I'm not interested in the sign so current is 1x 5 20 + 4 so it will be equal to it will be equal to what is it 4 + 4 which is 8 volts so 8 volt should be the answer let's check it out yes it is the correct answer I'm ignoring the minus sign because what will I do with that minus sign I'm just interested in the voltage difference that's all thank you pram all right moving on next question coming up on your screen gometer concept where most of the times the question comes on ammeter how do you convert ammeter into a sorry how do you convert a galvanometer into an ammeter and the idea lies in the fact that your galvanometer has some coil resistance this is the coil resistance and it can only allow some amount of current which is the full scale deflection current so if you have to measure huge current let's say that is I let's say that is I you bypass most of the current through another resistance called as the shunt resistance so this resistance will have a current of I minus IM Max through it and that's how you will be able to measure this without damaging the galvanometer this is the main concept and as you can see this resistor and this resistor are in parallel so mainly you will use RG is going to be parallel to the shun resistance so you can use all the concepts of parallel circuits like 1 by R is 1 by R1 + 1 by R2 or voltage difference is same or the current will be inversely related to the resistance anything every time you will get the answer don't sit and by hard any of these things it is useless just remember this diagram and understand the concept how you are bypassing it so usually this will be the range usually this will be the range of that ammeter this will be the full scale deflection current coil resistance shunt resistance this is how the values will be given to you is that okay yes is there any crash course for J Advance Plus the April attempt uh why is yes we do have the crash course for jmains plus the J advance and that is right over here in the description box as you are watching this particular video you can go down over here do you see J crash in English medium that is the one okay now this particular batch is right now there for 9.99 rupees all right it will be purely in English okay and you can see the batch has just started on 23rd December whatever lectures you missed you can watch it as recorded and you will get access till your J Advance if you clear meanss only then you'll be allowed in the Advan VCH that is natural okay so this is the batch which you can go for but if you want but if you want no sir I want it uh you know uh I want more features in this then you can go for crash Pro or crash Pro Plus where you will get printed material and oneon-one doubt solving this is the batch you can go for all right but if you are more interested in only Advance you think no sir Mains is okay sir I can clear it I know I just want only J Advance related com you know preparation then go for the aavia J Mains plus Advance this is the link click on this and you can see this particular batch starting February 2nd is for 14,000 rupees this is more on the advanced side always going to be Advanced side means is a byproduct of this but if you are interested no sir first I want to clear means then I will think about Advance then this is the J crash okay I have made it absolutely clear cool fine wise all right how do identify short circuits just see on a wire if there is a wire all the potentials are same if there is a wire connecting different points all those points will have same voltage number one if there is a line of symmetry then anywhere on the line of symmetry the voltages will be the same so if there is symmetrical circuit if you see this point and this point are exactly identical then you can sh them off you can connect it with the wire or if there is a device connecting them because the voltages are same you can disconnect them completely okay in fact you should check the lecture on equivalent circuits which I have done on the uh Channel itself just check this lecture out okay so on the hom page page only you will be able to see this is a complete physics playlist go down over here yeah just check this physics playlist go down almost all the chapters are there yeah where is current electricity yeah equivalent resistance and capacitance I have conducted a special class on just finding equivalent resistance and capacitance in that I have explained all the varieties of problem Cube problems short circuit problems symmetry problems non- symmetry problems which Stone everything is there over here just check that lecture out it will be very very helpful okay cool all right so let's do a question then so that you understand gometer is in series with 400 ohm uh okay measures a voltage up to 10 volts the value of the resistance to convert it into an ammeter to read up to 10 ampere is how many ohms a gal met of resistance 100 ohm when connected in series with 400 ohms measures voltage up to 10 volts just think about it this is your gometer which is of 100 ohms if it is measured uh in if it is connected in series like this then it can measure only up to 10 volts from this I think I can get the value of the maximum full scale deflection current because V is equal to I into R so it is RG plus that series resistance V is I correct so IM Max * 100 + 400 which is 500 so IM Max will be 10 / 500 which is 1 by 50 of an ampere okay perfect now you want to convert it into a amm okay so this is my gometer which is of 100 ohms this is your gometer okay it can only allow current up to how much 1X 50 of an ampere so now imagine you want to measure currents up to 10 amp so 10 amp current is entering in so you will bypass most of the current like this is that right bypass most of the current like this through a shunt resistance which value I do not know so out of 10 ampers 1X 50 amp goes here how much current will go over here it will be 10 - 1X 50 which is still going to be 10 ampers only because 150 is a very small number so ignore that small number so it is going to be 10 amp now since both of them are going to be in parallel so therefore the voltage drop will be the same which means the voltage across the shunt resistance will be R into I I is basically 10 voltage across the galvanometer will be R into I I is 1x 50 so from this what is the value of the shunt resistance 0 0 0 0 cancels so it will be 1X 5 ohms uh is that so just check this out something wrong 100 into 1X 50 is equal to RS into 1X 5 oh yeah it is fine the value of x is asked so if it is 1x 5 it will be2 ohm so it will be 2 0 into 10 ^ minus 2 ohms so the answer will be 20 correct because they have asked it as a number multiplied by 10us 2 so perfectly fine yes cool everyone shall we go ahead to the next question here it is gometer 200 ohm full scale deflection convert it into 20 milliamp range again similar question guys see what you will do you have a galvanometer whose resistance is 200 ohms full scale deflection current is 20 microamp you are sending in you are sending in how much current uh 20 milliamp of current you will bypass most of it you will bypass most of it like this so through this shunt so the current which will go here will be 20 milliamp minus 20 microamp which is then approximately 20 milliamp only now again use the same concept because they are in parallel therefore voltage difference will be the same so what will you say the voltage across the shunt will be IR IR is 20 Millie mil is 10 ^ minus 3 into resistance into resistance the resistance is RS is equal to is equal to current into resistance so current is 20 micro minus 6 resistance is 200 so the value of RS how much will it be 20 20 cancels yeah correct so 10^ - 3 10^ - 3 will also cancel yes so r will become 200 into 10^ minus 3 correct so 200 into 10^ minus 3 which will make it2 OHS so0 2 ohms is c for capto c for Captain stus perfect that is the answer very good disaster very good pan bhan anandu swaga Girish tgb very good awesome other yes C for captus very nice let's let's go to the next high weightage concept which is basically coming to AC circuits we are coming to AC circuits discussing impedances capacitive reactant inductive reactant power factor and special cases of course and the energy density which is stored inside an inductor okay so in AC circuits remember the voltage and the current may not climb up and go down together there might be some phas difference that phase difference comes because of either inductor or capacitor a resistor can never create a phase difference keep that in mind resistor will make sure current and voltage are in Phase now resistor although will not create phase difference but that is the only element which can cause the power to be lost inductor can store the energy in magnetic form capacitor can store the energy in electrical form so they two can't lose energy only resistor causes the loss of energy because in a AC the current voltages are varying continuously I am thinking is the voltage more or less so for that we Define something called as the RMS value RMS value gives me that value of voltage or current which will behave just like the DC deating the same losses so RMS is usually the maximum by root for a sinusoidal voltages so maximum Peak V byun2 or I byun2 so when I do that I byun2 or V byun2 that value is the same constant DC current which will produce the same loss as that of the AC current is that okay these are some basic things about AC uh you will have some frequency of the AC which is f and if you multiply 2 pi into F you will get angular frequency just like in shm waves and other things now a resistor resists the current inductor and capacitor do not actually resist the current rather they might resist the change in current or the flow of charges in some other way for AC and that is why you will have an equivalent resistance for inductor or for a capacitor which is called reactants now reactant resist the current for AC but it is not a resistor please mind it a resistance is basically the opposition to the flow of current and causes heat loss i s r but a reactance might oppose the AC current only but it does not cause heat loss so it is wrong to humiliate the inductor or capacitor by calling it a resistance because it is not causing heat loss so we give it a different identity called as reactance so XL is Omega L Omega is angular frequency L is inductance for inductor for capacitance the resistance equivalent is 1 by Omega C keep these formulas in mind now when all the three components are together resistance reactance for inductor and capacitor then together the total resistance to the flow can't be called resistance because one of it is reactant can't be just called reactance because one of that is resistance so that total factor is called impedence which is r s + XL - XC Square whole thing under the root if you ever get confused remember this triangle there will be resistance over here there will be net reactance which is XL minus XC over here and this triangle this will be Z which is impedence where this is the power factor so you can draw a triangle like this and this is nothing but Pythagoras Theorem then it becomes very easy okay fair enough all right moving on next one the power which is lost in that AC circuit is vrms irms into Cosi keep that in mind v r Ms irms into Cosi which can be also written down as I RMS s into r one and the same thing this cos f is called as the power factor this particular Cosi is called as the power factor of that AC circuit now keep this in mind the power factor maximum value can be one and when the power factor is one it is purely resistive circuit and such a circuit is set to be in resonance such a circuit is set to be in resonance in fact that graph of current versus different frequencies looks something like this when the power factor is one this is when the Omega value is 1 by root of LC for resonance you will have maximum current maximum power maximum power power factor will be one everything will be in sync you will see inductor voltage will be capacitor's voltage so the total voltage in the circuit will be just the resistive voltage all these things will come into place at resonance is that okay everyone right now like I said inductor stores energy just like capacitors store electrical energy half CV Square inductor store energy half Li Square half inductance into the current Square all right keep these things in mind so let's start with some questions coming up on your screen statement question just read the question question guys and tell me which one is the correct answer anandu if you are scoring 105 that means you need to see some more High weighted chapters you need to remove some of your silly mistakes you need to better manage your time for solving only those questions which you should do ignore the other questions Target 150 to 170 marks okay don't Target 200 also Target 150 160 marks like that and only do those chapters which will give you 150 170 marks enough and just do those Concepts practice many pyqs that will give you that confidence all right what do you think well the correct answer for this should it be option C where one is true but two is false reactance in a AC circuit is zero it is possible that the circuit contains capacitor and an inductor yes definitely reactance is zero that means it is possible it contains capacitor and an inductor because maybe XL and XC both are equal and opposite so the net reactance will be zero they basically end up canceling each other out definitely possible what about the second statement in AC circuit the average power delivered by the source never becomes zero never becomes zero the average power the average power delivered by the AC Source can never become zero no it can become zero in fact in this particular circuit the the resistance is zero so i^ 2 R is zero so the power is also zero on an average so it is zero so definitely in a AC circuit power can be zero if there is no resistance only inductor is there or only capacitor is there so can never become zero that is wrong so one is true but second statement is false yes option C no it is not option b good evening amuda yep if you are aiming for 170 by the way start with the next question if you're aiming for 170 I'm getting it what will be my all IND rank or percentile 170 marks will take you very close to 98 percentile that will be close to around 20 to 40,000 rank around that range that is what it will be also depends on how many students were there in your shift and all of that and competition this year is around 14 lakh we don't know April attempt whether it will become 14 lakh become 16 lakh or more so accordingly for that same percentile your all India ranking can change getting my point see 90 percentile or 99 percentile let's say for 10 lakh might be 10,000 rank but for 20 lakh 99 percentile will be 20,000 rank so the total number of students will also matter which we have to wait and watch how much it will be for the April attempt okay ranay good evening welcome back you can leave the math section Rago many students do that but don't expect more than uh 190 marks I mean theoretically 200 box but usually some mistake will happen 180 190 is usually the score even if you're a very good student and uh yeah so not trying to demotivate you but just telling you practically 180 190 is the limit of the score that you can expect which is close to 98 99 percenti coil of inductance resistance heat magnetic energy sto H it loses heat if it is losing heat where will it lose heat it will lose heat in this resistance so power will be i^ 2 R power is 64 current I do not know resistance is 4 so I square is 16 so I is 4 ohms why do I need this current because I want to find the magnetic energy the magnetic energy is half l i Square so is the inductance given yeah 200 mil mli is 10^ -3 current four so Square 200 200 by 200 100 into 10 ^ - 3 into 16 so this will be 10 ^ 1 so it will be 1.6 1.6 jewles perfect cool everyone that's right shall we go ahead to the next concept then all right let's go then let's go okay so we are coming to now re Optics all the formulas standard formulas which are there okay starting off with mirror formula lens formula and then lens maker formula and refraction through curved surface formulas usually they ask questions through that and uh sometimes they also ask questions on total internal reflection which I'll show on the next slide mirror Formula 1 by f is 1 by V + 1 by U also remember radius of curvature is 2 * of f magnification is minus V by U and also uh image velocity upon object velocity will be minus sorry uh will be minus v² by u s these formulas you must know and the power of a mirror is given by 1 by 1 by F but with a negative sign these are the formulas which are completely associated with mirrors whereas for lences 1X f is 1 by V minus 1 by U and the focal length is given by the lens maker formula where R1 and R2 are the radius of curvature of the surfaces of the lens this is relative refractive index so relative refractive index will be refractive index of the lens upon refractive index of the outside medium keep that in mind it's a relative refractive index if outside is there then n in the denominator will be one okay now for lens the magnification will be plus V by U same formula but with opposite sign image velocity by our object velocity will be plus v² by u s and the power of a lens in diopters will be 1 by F okay instead of minus 1 by f it is plus 1 if you don't have two surfaces you have a single surface which is curved then you use this formula so refractive index of the second medium by image distance minus refractive index of the first medium by object distance is the difference of the refractive indexes by the radius of curvature this is refraction at a single curved surface all right everyone okay very good awesome only yes mahalakshmi even if you just qualify J Mains doesn't matter or even if you get 99 percen in J me doesn't matter ultimately your J Advance all in the rank will decide whether you will get a particular branch in an i okay which is your J Advan rank J means percentiles ranks do not matter J means percentile and ranks only matter when you are taking admission in nit is government institutes triple it and all of that cool okay now the total internal reflection concept where you go from dense medium to the rare medium dense medium to the rare medium the sign of that critical angle is one by the refractive index this is one of the most important formulas which you should know okay total internal reflection concept questions do come in the examination right and of course snails law of course snails law snails law based questions can also come where you have S of angle of incidence upon s of angle of refraction is 1 mu2 which is mu2 by mu1 which is 1 by 1 by 2 mu1 which is speed of light in the first medium by second medium which is wavelength in the first medium by wavelength in the second medium this is by far the most elaborate formula sometimes they ask you question on wavelength sometimes they ask you to find the speed sometimes they ask you to find the refractive index relatively sometimes they ask you to find the angle anything is asked use this equation one of this will give you the answer okay very good moving on to some questions here is the first question on your screen object is placed object is placed over here and the question is if it is on the principal axis okay of the f FAL length 10 cm okay a plane mirror is placed on the other side at a distance of 20 cm image produced by the plane mirror is 5 cm inside the mirror the distance of the object from the lens is how many cmers that is the question all right okay yes class 10th uh reflection refraction Concepts can be used definitely Now read the question object is placed on the principal axis of focal length 10 cm plane mirror is placed at a distance of 20 the image produced by the plane mirror is 5 cm inside the mirror so the image produced by the mirror is over here this is image produced by the mirror which means most likely the Rays would have been coming like this oops the Rays would have been coming like this but they got reflected I believe or one second if the image is produced over here uh think of it like this the Rays were reflected like this so if you extend it here extend it here yeah it got reflected that's why the image was here so most likely so most likely the Rays were coming like this and like this so these Rays come here they get reflected here these Rays go over there and they get reflected like this that's why they were able to produce the image over here is that right my dear that means that means the lens was producing a real image over here a real image over here a real image over here which acted like an object for the mirror which acted like the object for the mirror thereby producing the reflection here so if it is mentioned in the question this is five cm how much will this be this will be also 5 cm which means if this is 20 how much will this particular distance be from 20 take out 5 so 20 minus 5 which is 15 cm that means the image distance is 15 cm for the length is the focal length given yes so use 1 by V - 1 by U is equal to 1 by F 1X 15 - 1 by U isal to 1x 10 it's a positive focal length it's a convex lens so 1 by U will be 1X 15 take 1X 10 on the other side so LCM is 30 15 goes two times 10 goes three times so this will be - 1 by 30 is 1 by U so U will be -30 CM which means this distance will be 30 CM negative because this is on the negative side yes perfectly yeah the answer is 30 cm from the lens cool that's how you can solve this question just doing some simple ray diagram gives an understanding of it yeah very good let's move let's move what is this radius of curvature of each surface of a convex lens having refractive index 1.8 is 20 okay radius of curvature is this much the lens is imer in a liquid of refractive index 1.5 the ratio of the power of lens in air to that in the liquid will be something is to one what is that value of x approximately so when you are in air the power in air will be one by focal length in air which is refractive index of that lens which is how much 1.8 so minus one this will be 1X R1 - 1 by R2 that will not matter eventually when you are in that Medium it will be 1 by F of that Medium that will be relative now so 1X 8 by 1.5 minus 1 remember I had told you this refractive index is always relative refractive index of lens by refractive index of the medium again this will be 1 by R1 minus 1 by R2 over here 1 by R2 over here so this will be nothing but okay leave it as it is now they have asked you what is the ratio of the power so divide both of them so divide both of them power in air by power in the medium this will anyways get cancelled out so 1.8 - 1 by 1.8 by 1.5 - 1 this is8 this is 18 by 15 18 by 3 is 6 6 15 by 3 is 5 - 1 8 is 8x 10 * 6X 5 - 1 what is it 1X 5 so this will be 8 into uh 8 divided 10 by 5 10 by 5 is 2 8 by 2 is basically 4 so it will be basically 4 is to 1 so answer should be four yes the correct answer is four got it everyone very good these kind of questions and models are very very common let me tell you that yes they are very very common very good let's go to the next concept my dear Warriors questions on constructive destructive interference in light waves the intensity relation The Fringe width and all these concepts are very common every time you will see this see you can always argue sir that question is also important this concept is yes you can find then you have to sit and study the all the chapters all the concepts all the lines but like I said we are doing all the important things over here there might be few things here and there but that's okay we are concentrating on things which will definitely give us is 99 percentile all right so here we go part difference for Young's double slit experiment is D sin Theta D is the distance between the two slits of the double slit experiment if it is constructive the path difference will be integer into Lambda Lambda 2 Lambda 3 Lambda 4 Lambda like that but if it is destructive interference minimum intensity dark fringes then it is odd times Lambda by 2 because this will become 2 n + 1 2 n + 1 is always an odd number so odd times Lambda by two that means Lambda by two Lambda 3 Lambda by2 F Lambda by 2 that is what the destructive interference will create if you want to look at any n Fringe bright or dark for bright Fringe use n * Lambda d by D for dark Fringe or number times Lambda by 2D that's what you will use and that will also give me The Fringe width which is Lambda d by small D wavelength into distance from screen to the slits upon the distance between the slits keep this in mind apart from this you should know that the amplitudes act like vectors if you have amplitude one amplitude two and this is the resultant amplitude then uh if you know the part difference this part difference can give you the phase difference like this you multiply it by 2 pi you will get the phase difference and the resultant amplitude is A1 s + A2 s + 2 A1 A2 cos Delta 5 the whole thing under the root like vectors similarly you can get the intensity which is i1 + I2 + 2un i1 I2 into cos Delta 5 that is your resultant intensity keep this in mind also intensity of any light wave or any wave is always directly proportional to the amplitudes square amplitudes square if you have constructive interference that means Delta X is Lambda 2 Lambda 3 Lambda in general n * of Lambda then the amplitude is maximum which is given by A1 + A2 and the intensity is also maximum which is root i1 plus root I2 the whole Square whereas if you are talking about destructive interference that means Delta X is uh .5 Lambda 1.5 Lambda 2.5 * Lambda like that or time Lambda by 2 then amplitude is definitely the least it will be A1 minus A2 modulus because I don't know who is big and the intensity will be minimum and it will be given by root i1 minus root I2 the whole Square cool that is what destructive interference these are all important Concepts from waves interference light Optics all of that let's see some of the questions there are two wavelengths in a ydsc the distance between the slits is this much between the screen is this much the least distance where the fringes will coincide is where exactly very interesting because there are two lights now what happens is over here imagine this is your screen imagine you are seeing you are seeing the bright Fringe over here okay of a particular wavelength and another wavelength is also there but that Fringe width is not so big so what happens The Fringe which is small will repeat very often some something like this will repeat very often something like this whereas The Fringe which is little bit bigger will repeat little bit less often something like this and the distance will also be different but somewhere or the other they will again coincide isn't that right somewhere or the other again they will coincide maybe after certain fringes initially they are coinciding then they go offset offset and then finally they will coincide that is what will happen my dear Warriors so when they coincide so if this is basically your Central Central bright Fringe let's say they will coincide over here this is N1 Fringe of let's say wavelength one of wavelength one and let's say this is the end to Fringe of wavelength number two this is where they essentially coincide where they coincide wherever they coincide I can say that their coordinate will be the same so the y coordinate will be equal for both the fringes what is the formula for y-coordinate I just give it to you right over here I just gave it to you right over here for the N bright Fringe n Lambda d by d n * of Lambda d by D guys so just use that so this will be N2 Lambda 2 D by small D this will be nothing but N1 Lambda 1 capital D by small D DD DD cancels so N1 by N2 will be Lambda 2 by Lambda 1 wavelength 2 is 550 0 55 0 0 wavelength one is 7 0 0 0 0 0 0 0 cancels over here correct so N1 by N2 will be well with five it goes 11 times with five it will go 14 times so this will be 11 by 14 that means that means what the 11th Fringe of 7,000 amstrong coincides coincides with coincides with whom with the 14th Fringe with the 14th Fringe of 55 0 amp that is the meaning of it so in order to find now what is that particular y coordinate particular y-coordinate either use this or use this it's completely up to you let's say you use this N1 Lambda d by D anyways this is equal to this so N1 is basically 11 Lambda 1 is 7,000 amstrong so 10 ^ -10 distance between the slits is this much and from the screen how much is it 1.5 M which is 150 CM small D is 2.5 so 2.5 10^ -3 that will give you the y-coordinate which will come out to be 462 which will come out to be 462 okay so 4 62 into 10 the^ -5 met is that okay my dear Warriors yep great yeah awesome awesome how much time more maybe 30 40 minutes not more than that yeah coming to the next concept yes we are on to Modern physics so guys not more time is left yeah we'll finish this fast only on time so already 7 hours are over of teaching so 7 and a half hours maybe okay D brogly wavelength electron de brogly wavelength kinetic energy and de brogly wavelength and relation between the D Broly wavelength and momentum yeah are these questions of means level Yes means medium level simple easy and medium I'm not taking tough questions today I'm telling you this openly or else you'll expect certain old tough questions but actually the questions are easy no I don't do all all those nonsense things there is a separate session which I made with difficult questions and also the N abas questions are very tricky I hope you have seen both these sessions if you have not seen now please check it out it is there on the channel only yeah just go to the live section see just few days back J means NTS favorite questions these have good average and difficult questions if you are specifically looking for the the difficult questions of where did it go are huh difficult questions right over here then it is over here for J if you want only easy questions that session is also there everything has been already made on the channel okay so just have to go through it h All Right Moving On Moving on De brogly AA you are saying that these questions are are very difficult or you are saying that these questions are very very easy you should tell me that error 404 as per Main's perspective any particle which moves has momentum and it is given by mass into velocity but a particle not only possesses momentum it has a dual Behavior which is a wave like Behavior just like light the light is an electromagnetic wave having wavelength amplitude frequency wave speed and all that characteristics of a wave like defraction interference right all these things but it also possesses light also possesses particle Behavior which is called as a photon photon is the energy packet of light it has a Quant of energy given by HF H being the planks constant similarly de Broly hypothesize that just like light can behave like a wave and particle even a matter can usually show particle Behavior but under certain conditions you can see the wave Behavior which is called as the matter wave this matter wave is not electromagnetic it is not gravitational it is not nuclear it is a separate kind of wave this matter wave has a wavelength given by H by P H being the planks constant P being the momentum usually the questions are on electrons and all of that so usually when you have electron this momentum by the way can be written down as 2 MK because kinetic energy is momentum Square by 2 m so you can write it down like this but usually this kinetic energy comes because you have accelerated the particle charged particle like electron or proton so this kinetic energy usually is is going to be uh the charge which is e into the voltage so then you will get this formula but for an electron mass is known charge is known H is known two value is known so the wavelength of D brogly for an electron accelerated is given by 12.27 byun2 root V this wavelength is going to be nanometers yes this wavelength is going to be in nanometers is this clear everyone okay very good awesome next important thing next important thing oh okay directly with problems because D Broly does not have much things so usually you will see D brogly questions are there either they will combine it with magnetism where the particle enters a magnetic field of radius R MV by QB or they will give solo question or they will comp it with electrostatics where kinetic energy is charg into potential difference usually 90% of the times these questions are there as it is electron Photon same energy ratio of the wavelength of electron to that of the photon is how much okay ratio this question was very popular let me tell you guys this was asked many times in different different ways in many many uh you know exams or shifts so electron of mass m okay has energy e and Photon also has energy e so if you talk about the photon first that energy is HF which which is also H C by Lambda okay the ratio of the wavelength of electron to that of the photon so this is the wavelength of the photon so Lambda P will be H C by E keep this on the side then let's go to electron also has the same energy H Lambda of electron is H by H by P but P can be written down as < tk2 M into e okay so this is Lambda of electron the question is something else you have to find the ratio okay so the ratio means Lambda P by Lambda e this is equal to H C by E and this will be nothing but H divided root of 2 m so let's see what do we get H H cancel cunk 2 m this is root e upon e root e root e will cancel so you will get root > 2 m by E that is your Lambda P by Lambda e so C is there obviously and you also have 2 m by E over here so that's it that is option b I believe because they have asked electron by proton electron by phon so Lambda e by Lambda P will be 1 by C this will be e on the top and 2 M below yes e on the top and 2 M below this is B option is that right everyone very good all right all right very good we can do next question guys uh before going to the next concept there was there are these common questions which are based on proton electron Neutron and all these things so let me tell you this very clearly let me tell you this very very clearly see when you talk about proton the mass is m charge is positive Neutron ion okay proton is same as H+ H+ Neutron is nothing but your positively charged isotope of hydrogen mass will be 2 m m being atomic mass unit charge will be still plus e then you have alpha particle alpha particle has mass 4M charge will be+ 2E keep this in mind whereas when you have an electron when you have an electron okay the charge is negative the mass is negligible the mass is negligible it's very very small whereas positron positron just like electron same mass as of electron but the charge is going to be plus e these things you must know for solving most of the problems yes alpha particle is nothing but helium double no helium plus helium uh sorry helium dou plus yeah is that okay all right now what kind of questions do come on this like say for example the question is like you know an alpha particle and a proton is accelerated through through voltage V and 2v and they enter a magnetic field which is perpendicular find the ratio of their radii of their Paths of their paths number one also the question can be the ratio of their D brogly wavelength D Broly wavelength these kind of questions are very very common so let's try to solve this first things first if you want to find the ratio of the radar of their paths once they enter magnetic field radius is given by mass into velocity divided Q into B charge is different mass is different speed is also going to be different remember these are not speeds these are voltages so be careful so how do I find the speed let's think first of all the kinetic energy will be coming from the potential energy so kinetic energy will be the charge into the voltage difference uh sorry kinetic energy will be half M velocity Square potential energy will be the charge into the voltage difference okay so V will be root of 2 Q Delta V / M so use this over here so use this over here < tk2 Q Delta V / M so R will be equal to m v is this one divided by QB therefore what will happen mm will cancel QQ will cancel only 1 by B will remain and here you will have 2 Delta V charge charge will cancel so Q will come below mass mass will cancel mass will remain Below in the root this is what it will be from this you will understand that radius of alpha by radius of proton will be directly proportional to voltage differences so voltage difference of alpha by voltage difference of proton directly proportional to root of mass so mass of alpha by mass of proton inversely proportional to root of charge so uh charge of alpha below charge of proton over here what is the voltage of alpha alpha is basically V of proton is basically 2v mass of alpha is basically 4 M of proton is M charge of proton is e of alpha is 2 e so what will this be 1 by < tk2 into < TK4 is 2 into 1 byun2 < tk2 into < tk2 2 2 2 cancel so 1 is to 1 the answer will be 1 is to 1 the radius will be the same is that right everyone okay all right we will I will confirm that AI te I also got that notification saying that there are some rumors saying that the State Board entrance examinations will be preponed I I was also surprised let me just complete the session and then I will talk about it the next part of this problem the next part of this problem is comparing the D brogly wavelength so how do you do this particular question observe now the D Broly wavelength is planks constant by momentum momentum is root of 2 m k and the kinetic energy is nothing but charge into the voltage difference so from this what do I get wavelength of D brogly of alpha by the proton H is a constant 2 is a con Conant these three are CH changing inversely proportional to root of mass so mass of alpha below mass of proton on the top charge of alpha below charge of proton on the top voltage difference of alpha below voltage difference of proton on the top because they are all inversely related so let's do this proton's mass is m alpha will be 4M charge of proton e of Alpha 2 e voltage of proton 2v of alpha it is V okay so this will become 1 by two this will become 1 by < tk2 this will become root2 Roo tk2 root2 cancel so this will become 1 by two so this is 1 is 2 so the wav length ratio will be 1 is2 okay yes the PDF will be available with the annotations don't worry about it cool let's go to the next concept of photo equation photoelectric concept which was done many times on this particular Channel remember when light falls of a particular wavelength or a particular frequency such that the energy of the photon is more than the minimum energy to suck out that electron on That Metal then electrons are rejected with some kinetic energy there is a range of ktic energy is from zero to maximum the luckiest of the electrons have maximum energy but most of the electrons have little bit less than the kinetic energy maximum value now the minimum frequency required to start the photoelectric effect is called the threshold frequency and the wavelength is called threshold wavelength and that minimum energy is called as the work function f work function f that work function will be h f not F being the threshold or H C by Lambda not Lambda not being the threshold wavelength critical wavelength this is Maxim energy this is the energy of the photon so energy of the photon is work function plus K Max over here okay now remember energy of the photon can be written down as H C by Lambda or HF this is equal to work function which can be written down as HF KN or H C by H C by Lambda KN or you can write it as HF not and over here kinetic energy maximum can be written down as half m Vmax square or you can write it as electron charge into the stopping potential now what is the stopping potential these electrons which are ejected out they have some speed to stop them you apply a voltage to decelerate them so that voltage which is required to decelerate them completely is called as the stopping voltage now interesting thing is when you increase the intensity of the light the number of photons will improve but that will not change in any manner the stopping potential nor will it change the work function nor will it change the cut off frequency or that uh any of these values the only thing which it affects is the number of electrons which will decide the photo current so the current in the circuit is directly related to the intensity of the light which is directly related to the number of photons or the number of electrons otherwise intensity does not play any role it can't change the cut off it can't start the photoelectric effect if by chance the energy of the photon is not sufficient to Kickstart that photoelectric effect keep these things in mind so this is the main photoelectric equation and you'll be most likely using this all right most of the times let's see some questions based on this if two metals are exposed to radiation then the work function are 4.8 and 2.2 then choose the correct option wow this is not that difficult at all I'm pretty sure you can crack this come on my dear Warriors yep oh come on think about it two metals are exposed to radiation of 350 nanom now 350 nanom let's find out the energy of that Photon first that is 1 2 4 0 divided by Lambda this formula you can use instead of C usually what the formula is is H C by Lambda right but you know the value of H C let's say Lambda is in Nano and you want to convert it into electron volt then it is 1 2 4 0 divided by Lambda provided this is in nanometers and the final answer will be in electron volt so just substitute that 1 2 40 divid 350 how much will it be how much will it be approx approximately approximately some 3 something approximately it will be 3 approximately 3 electron volt it is not exact but approximately 3 electron volt so now look at these two values obviously you can see 4.8 electron volt is more than three so photoelectric effect will occur but this guy 2.2 is less than three so no photoelectric effect will occur because the energy of the photon is lesser than than the threshold that's very very important so metal a will uh what is it metal A and B okay metal B will not emit photo electrons metal B will not emit photo electrons yes I hope this is absolutely clear yes metal B will not emit photo electrons that is the correct one both will emit that is wrong both will not emit that is also wrong then there can be one more type of question which I have seen let me show that to you which is very commonly asked it will be like for wavelength Lambda of the photon which is incident the stopping potential stopping potential is V if the wavelength is let's say 2 Lambda if the wavelength is 2 Lambda then what is the stopping potential or let's say the stopping potential is given and they ask you the work function things like that they are very very common let's say the stopping potential is now 2v Chum I'm just giving some random things and then they will ask you what is the work function or what is basically the threshold wavelength these kind of questions are very common so what you do in such things first situation you take first situation energy of the photon is H C by Lambda work function is 5 plus uh e into V plus e into V second time second situation what is it h c by 2 Lambda is work function plus plus the stopping potential because the wavelength has increased the frequency has reduced actually let me do one thing I've not chosen proper values let me choose proper values that will be better let's say the stopping potential is 2v here when this is 2 Lambda then it is V now it will be fine okay so now let's get back for wavelength Lambda stopping voltage is 2v so energy of photon is H C by Lambda work function plus e into stopping voltage second situation H C by 2 Lambda the work function is five stopping voltage is just V this is the two equations that you will get once you get these two equations what can you do just subtract them just subtract them you will get a beautiful equation H C by Lambda minus HC by 2 Lambda 55 will cancel so it will be 2 EV minus EV so therefore from this therefore from this what will you get HC by 2 Lambda is equal to just e into v h c by Lambda is just basically e into V use this over here use this right in this particular equation so H C by 2 Lambda is work function plus EV EV is nothing but H C by 2 Lambda in this case the manner in which I have chosen the work function is just coming out to be zero I mean looks like invalid okay but I had chosen some random values like I showed you but if I chose proper values obviously I'll get a good value of the work function but otherwise I hope this is clear how to solve these questions yeah how is the last question answer a isn't it d uh if two metals A and B are exposed to radiation okay and the work functions of the metals A and B are 4.2 and 2.2 this is the work function function oh oh oh oh oh this is the work function this is not the energy of the photon I am so sorry guys yeah I'm so sorry I'll just uh redo so sorry that is what happens when you teach for more than 7 hours I believe this was the work function this was not this was not the energy of the photon my bad my bad my bad so sorry now this three electron volt was the energy of the photon okay the energy of the photon was three so if you see the energy of the photon is more than the work function here actually so 3 electron volt is more than 2.2 electron volt which is the work function this is the energy of the photon so photoelectric effect will occur in case of B in case of B but if you see a this 3 electron volt is less than 4.8 electron volt this is the energy of the photon this is the work function so it will not occur so that is the case of a so in a it will not emit the photo electrons yes that should be the correct answer Let's see we didn't even check the answer I think oh yeah the answer was D actually yeah yeah you're right it was D perfect so very nice question I mean sometimes Photon energy is given sometimes work function is given so you need to compare it properly or else you will get exactly opposite answer so this is what happens silly mistakes yes awesome thank you Girish for pointing it out just slipped through our mind okay so guess I need a break now okay we are almost nearing the end the last concept is coming up okay what do we have what do we have Gates all the gates 100% there is a question in your jmains logic gates electronic devices true tables logical operations and or nor n not exort all these things so you should know the truth tables for everything see basic thing is if you have Orit I think is it there somewhere it's not there anyways see when it is or gate which looks something like this at least one of them should be true 0 0 will give you 0 0 1 will give you zero sorry 1 1 0 will give you 1 1 one will give you one so the operation for that is you know the output will be a plus plus b that is the Orit anyone is true the output is true similarly when you have a and operation and operation the symbol for that is like this symbolically you write dot a do B so 0 0 will be zero both should be true only then it is correct so when both are true then you will get one similarly you have the not gate which is like this so the output is written down as a bar and if it is zero the output is one if this is one this is going to be zero this is the true table for a not gate okay when you have nor operation when you write this as nor gate nor then instead of zero you'll get one here you will have 0 0 and zero that is when you put a dot over here similarly when you put a land operation you put a dot here then instead of zero you'll get one one and instead of one you'll get zero and here instead of a do B you'll put a b bar instead of a plus b you'll put a plus b bar apart from this there are two important theorems which you should know also called as D Morgans theorem D Morgans D Morgans theorem which will help you a lot that is a do B bar is a bar + bar bar and A + B whole bar is a bar dot b bar this is very very useful this is very very useful is that clear okay Manish what to do yeah all right yes I know it is 6:30 all right cool let's go let's go let's go do some questions for the given logic gates which is the correct root table let's see if you guys can figure this out what is it going to be this is a a is also going over here this is b b is also going here this is a bar this is bar bar this is a bar. b this is andg this is a do bar bar this is orgate so it will be a bar do B plus a do bar bar you know which operation is this this is called as a exor operation XR exclusive or exclusive or means exclusively they should be different means 0 and zero will be zero it's like Orit one and one will also be zero only when these are different only then it will be one this happens only for exor Target exclusively or it is not exclusive here it is not exclusive here it is exclusive here both are different then it will give correct output so which is the correct one over here yes it is I think D option 0 0 1 1 0 0 1 1 Z both are giving one one yes it is option number D cool remember this as a theorem only exclusive or is a bar. B plus a. B bar that is exclusive or gate yes awesome awesome okay cool let's go let's go let's go okay we are done with this and uh please remember those of you who want to join our J crash course for April attempt it is still open it is also going to be valid for J advance and if you just want the test series that link is also there in the description box I'll just show it to you and uh where is it where is it where is my session yeah there you go now the best part about that test series is that yeah the best part about the test series is that it can give you access for not just Mains but also Advanced and also you have the test series for all India entrance examinations like bitsight VI e srmg uh comedk uh J Advance EAP sat iser everything is there allinone test series and this is available for 16667 okay and for your Just J Test series Mains and Advance only for April as well as the mains in January attempt as well as the advance it's for 1,333 both the links are there in the description box okay now I hope today you enjoyed this session also you learned a lot from this session I have covered major topics major Concepts from all the chapters as much as possible there is one more interesting session which you might have seen last year and that is something which I feel you should do just search for formula in the search bar you can search formula Shas sir also you will see either this session or you can just search for formula physics formula physics St sir then po where is it yeah see this complete formula rision this is 11 months ago 6 and a half hour class again yourr is known for it this has all the formulas and the best part you know about this session it has it has the PDF also yes it has the PDF also for all the formulas in this PDF it's not just for high weightage or important chapters all the chapters are there all the formulas are there so you can revise through my notes right over here okay so just search for this particular session keep in mind this particular thumbnail which is that thumbnail it is this one okay this 11 months ago 6 hours 46 minutes check that out yeah cool so I'm pretty sure after this there is no reason for you there is no reason for you to complain I mean any any person with even low score or even with a person with no confidence after this session I'm pretty sure your confidence level will be on the top it should be Top Notch okay just solve questions just do mod test just revise formulas Focus only on what you want not what you should get based on others don't have to force yourself for 99 don't force yourself for 95 or 90 percenti if you think no sir this time I think you know have not done enough preparation I will focus 85 percen next time I will get 99 percentile okay but make sure you get that 85 it should not be like you are trying to get 99 and instead of 85 you get 60 percenti that is what I mean so please understand that you might think that okay this paper will be easy that paper will be difficult nothing works in that examination Hall all these statistics analysis this is whatever you do at the end of the day is more or less only for your preparation not in the exam Hall in the exam Hall what matters is are you able to crack that question if you decide I'm going to solve only 14 or 15 questions per subject so totally I will solve 45 questions that's okay perfectly fine maybe five questions will go wrong 40 into four will give you 160 marks five questions have gone wrong you'll get 155 marks still so just by solving 15 questions per subject you can still get 155 marks which is 96 percentile around understand that 96 97 yes close enough to that percentage so guys it's all about strategy it's all about believing in what your plan is your plan may not work for others others plan may not be effective for you so believe in your ideology and go through the you know entire rigorous process for the next 5 seven days or 10 days depending on when your shift is I'm pretty sure you will crack this particular examination all right this is just a stepping stone for most of you I know next time in April attempt you will do even better but don't think about it now for now this is what I have to do January attempt is my last attempt think of it like that and try to push as much as possible because today you do a small amount then you you have to work harder for the next attempt now you work hard so you will have to you know cover up very little for the next attempt push yourself let yourself free I'm pretty sure you will do really really well okay so with this I shall take a leave make sure you like this video share this video subscribe to the channel leave a comment after this video how you enjoyed this session okay bye-bye take care have a great time