hello my dear students welcome to PW English medium class 9th and 10th YouTube channel my name is ashoke iski I'm your physics teacher students in Phoenix batch already we have completed first two chapters that is a motion and forign laws of motion and today we are going to discuss about a third chapter in physics that is the gravitation okay so without wasting a time let's get into the topic so today we are going to discuss about you know third chapter in physics that is a gravitation and a subject that is in science we are talking about a physics portion that is a third chapter gravitation and the batch name you can see Phoenix and this batch is purely for class 9th students of cbsc board okay and this is going to be our one short lecture that means we are covering all the concept in one stretch okay so that means we are covering entire anxiety topics in this particular chapter okay so that in today's topic we are going to cover the first topic that is universal law of gravitation after that acceleration due to gravity then we are moving with mass and weight so here we are going to uh discuss about what is the difference between mass and weight and and the last one pressure okay so pressure in solids pressure in liquids pressure in gases and the last one archimed principle so this archimed principle is very important okay so by this concept we get to know why the some bodies floats on the surface of water some bodies are submerged inside the liquid and some bodies sink to the bottom in the liquid okay so let's start with a very first topic that is universal that is universal law of gravitation okay so before that in the first chapter we have learned about you know motion where we have discussed about you know so many parameters with respect to motion like distance displacement then speed and velocity then acceleration in the second chapter we have discovered what is the cause of a motion that is you know Force so after that we have discussed the laws of motion that is related to Newton's Laws of Motion that is a total three three in the numbers okay Newton's the first law Newton's a second law Newton's a third law okay so Newton's a first law indicates you know qualitative discussion of a force and Newton's Second Law discuss you know quantitative discussion of a force and Newton's third law which IND indicates or discuss about you know the nature or behavior of a force okay now here before starting inversal iners the law of a gravitation here we have a some question okay we have a some questions the first question the first question why there is a motion of an object means what is the cause of motion of object okay what is the cause of motion of an object body or particle and the next one why there is a change in a speed or velocity of the body okay that means if the body is moving with a uniform velocity or speed okay so if there is a change in a speed what is the cause of it okay and if you throw anything vertically upward or anything when you throw vertically upward White is coming back to the center of Earth means why it is coming down why there is a Apple okay there is a Apple why it is a falling down when it is detach detached from the branch of the tree okay and here we have a few more questions with respect to you know these diagrams what is the cause of you know revolution of these satellites why these satellites you know revolve around the earth and here we have one more you know example why there is a revolution of Earth around the Sun or else you can say what is the cause of revolution of a planets around the Sun okay so what is the main reason all the planets go around the Sun what is the reason the moon goes around the Earth in all the examples in all the cases we can include the cause main cause is that is the force that already we have learned in the second chapter okay in all these cases there must be some force acting on the object the planets and on the moon your example I have considered here Earth Earth that is a planet and here satellite n natural satellite for our Earth that is the moon right okay now we got to know if there is a motion if there is a change in a motion means if there is a change in direction if there is a change in velocity or if there is a change in a speed the main cause is that is a force and there are few more example if the body initially in the state of rest if it is coming into the motion what is the cause of it still it is a you know Force if the body is a moving you know some certain speed say 100 km/ hour okay if it is a Keyon on reduces the speed keep on reduces what is the cause again the reason is a force okay and in this two particular cases that is the one Earth another one is a satellite okay if they are revolving around here if you consider this Earth is revolving around the Sun and these satellites are revolving around the earth what must be the reason what is the cause of it still it is a force but what type of force that is a gravitational force okay so we are going to discuss about you know this gravitational force in detail okay now so here there is a one scene okay here we have a you know a Newton already you people know that that is a Sir Isaac Newton okay so just imagine one day okay it is like a story based okay one day Newton was sitting under the tree okay so one apple detached from the branch of tree at a fall on head of the Newton was like what it checked that was Apple and he hold that apple and was thinking why this apple fell on my head okay if that is the force if apple is attracted by the Earth and why can't this apple also attracted towards that apple means if there is a force okay if there is a force between these two means one is Earth and another one is Apple if Earth is attracted that Apple towards it okay why can't this apple attract this Earth towards Apple this was the question raed okay and he concluded by the Newton's second law that is given by FAL to ma a yes of course there is a force between apple as well as the Earth it is the same force that is a gravitational force and this is equal in a magnitude means whatever the force exerted by the apple on the uh Earth the same force exerted by the Earth on the Apple but in this case what happened the Apple fell down means Apple moved towards the Earth but Earth did not move towards the Apple what is the reason again it is the Newton's Second Law what does that Newton Second let says the force produced okay the acceleration produced in a body is a directly proportional to the force okay and if there is a more Force there will be more acceleration if the direction along the motion of the body okay if it is opposite then the acceleration will reduce okay that we call it as a retardation and if you want to eliminate this proportional proportionality you have to add proportionate constant that is the m a m is the mass of the body okay and if you consider the same force acting between Earth as well as a moon sorry Earth as well as a apple okay let me consider force exerted by Apple okay force exerted by Apple so here mass of the apple and acceleration of the Apple okay in the same way force exerted by the Earth okay force exerted by the earth that is equals to mass of Earth and acceleration you know produced in a earth okay that is a according to uh Newton's third law okay according to Newton third to every action there is a there is always equal and opposite reaction if this Earth is exerting a force on Apple that means apple is also exerting a force on Earth equal in magnitude but opposite in direction if I consider that concept okay so force due to Earth and force due to Apple okay so by by the concept if you see okay so that is force due to Earth if you consider force due to Earth if I consider that is the mass of the Earth and acceleration produced by the Earth okay and the same way here f is a constant right in both the cases let me consider a constant okay this is the constant so this can be written as me AE and acceleration produced in Earth is is inversely proportional to the mass of the Earth in the same way if I consider ma acceleration of Apple okay acceleration of Apple if I consider that is inversely proportional to the mass of the apple and if we consider mass of Earth is much much greater than mass of the Apple okay mass of the Apple so more the mass less will be the see if acceleration okay if it is a more that means the mass of Earth is less okay okay so not earth just I'm writing acceleration if it is more that means mass is less okay if acceleration is less mass is more inversely proportional if you compare mass of the Earth and mass of the earth as well as the mass of the Apple here we can consider you know mass of the apple is negligible compared to the mass of the Earth yes of course there is acceleration produced in the Earth but it is comparatively very very small so that is the reason Apple fell towards the center of Earth and this Earth do not move that means there is a motion but very very small slightly you cannot imagine okay you can consider it as a negligible okay so therefore we can observe only apple is moving towards the Earth not earth is moving towards the you know Apple okay got it so let's uh you know read this statement once uh Newton was sitting under a tree and apple fell on him the fall of the Apple made Newton start thinking he thought that if the Earth can attract an apple can it not attract the Moon is the force the same in a both cases it conjectured that the same type of force is responsible in the both cases e argued that at each point okay of its orbit the Moon here they have considered instead of Apple they have considered Moon okay so this is the moon and this is the earth okay Moon Falls towards the Earth instead of going off in a straight line so it must be attracted by the Earth but we do not really see the moon Falling Towards the Earth reason me that is the mass okay got it now next topic that is the centripedal force centripedal force okay so let's consider okay let's consider this is the circular track circular track of radius R okay fine and if I consider one particle if I consider one particle okay if I consider one particle this is the particle and the particle is in motion so at this particular position what is the direction of velocity you can see this is the direction of velocity okay so this is the motion of the Vel particle or a direction of velocity okay so this is how it is moving but what is happening instead of a moving straight path it is a moving in a circular track how can we know that it is moving in a circular Track by the path okay at this particular Point add this particular Point okay let's uh you know consider a Four Points around the you know circular track and add this particular Point Okay add this particular point in the direction of a motion of a particle this okay so this is the direction of velocity and this position the velocity of the particle in this direction and add this particle okay so this is the direction of velocity okay this is the direction of velocity and here you can observe at at every interval of a Time the particle keep on changing its position and we can ask sir what is the reason for that why it is not moving in a straight path why it is taking a turn or else why it is changing its direction at every interval of a time that we have learned in the last chapter right so that is you know there is a force act in on this particle towards the center of the circular path okay so here you can consider there is a force acting towards the center of the circular track that we call it as a centripetal force okay centripetal force means centripetal force okay centripetal force centripetal force means Center seeking force center seeking Force okay centripetal force is nothing but Center seeking of force so this is the main reason why the particle keep on changes its direction at end at every interval of a time so it is a circular path and just imagine if there is no centripetal force what will happen this particle move tangentially or else this particle will move in a straight path am I right just imagine uh take a you know one thread and tie with a stone okay tie the stone with a thread and start revolving it okay so that stone will be performing a circular motion okay circular uniform circular motion if you leave that thread okay if you leave that thread what will happen it will move a tangential in a straight Direction yes or no and what is the reason before it is it was moving in a circular path but after you leave it after you break the thread after you remove a centripedal force it is a moving a straight path so that means if there is no force acting on a particle it would have move in a straight path instead of a circular motion right so main cause of this uniform circular motion that is a c Ral Force okay and on this particular you know position okay in this particular position let me consider this particular position there are two forces are acting okay there are two forces are acting and already we know that the first one is the centripetal force and the next one centrifugal force okay centrifugal force this is the centri centrifugal force okay centrifugal force this is the centrifugal force okay so this is a centripetal force and this is the centrifugal force then what about centrifugal force centrifugal force centrifugal force okay centrifugal force centrifugal force means Center means the force seeking away or the force acting away from a center of the circle okay Center of center of seeking force center away seeking force that means if there is no centripetal force the particle would have move in a straight path means it is always moving away from the center of the circular path so that is the reason we call it as a centrifugal force and washing machine okay washing machion will be worked on the principle the centrifugal force okay washing mission got it and it is not required for your you know class 9th you know syllabus just I'm giving information got it now centripetal force and centrifugal force it is understood that means if there is any particle or body or an object if it is a moving in a circular path how many forces will be acting two forces will be acting what are those forces first one centripetal forces that means Center seeking Force the next one centrifugal force C away sing of force okay so what is the magnitude the magnitude of a centripetal force okay centripetal force I'll write FC and FCF okay centripetal force and centrifugal force are equal in a magnitude okay equal in a magnitude but opposite in direction equal in magnitude but opposite in direction okay oppos opposite in direction when the equal forces are acting but opposite in direction what is the net force on this particle so here net force on the particle will be zero so that is the reason it is keep on moving a uniform circular motion okay if there must be a change in okay if there is must be a change in velocity okay so why because it is keep on changing its direction it is moving with the some speed okay we understood okay we understood it is changing its a position at every interval of a time that means in this particular situation speed is a constant okay speed is a constant sir how can you say that speed is constant let me write speed is given by distance divided by time taken okay let me write a distance divided by time taken and what is the distance for one complete circular path okay one complete circular path we can consider circumference of a circle right what is what is the circumference of a circle 2 pi r divided by because radius R and a time that is the T see radius is constant and just here you need to substitute the time at every interval of a time what is the speed okay so speed will be given by you know uh this is the distance divided by time distance is nothing but circumference of a circle that is the 2 pi r and give divided by time so this is the speed and what about velocity velocity is the changing velocity is a changing velocity changing okay reason because the direction because the direction at every interval of a Time the direction of the particle keep on changes here you see it is a North here it is a West here it is a South here it is a East got it so because of a change in Direction you can say that the particle is in a change in a velocity why I'm calling it as a change speed is the same means the magnitude of the particle magnitude of a velocity or you can say directly speed is a constant but as it is changing a direction if we consider a speed along with the direction we call it as a velocity so therefore can I write change in a velocity yes change in velocity Whenever there is a change in velocity you can call it as a acceleration of the particle acceleration here here acceleration is there so uniform circular motion okay uniform uniform uniform circular motion uniform circular motion is accelerated motion accelerated motion even though speed is constant but the velocity not okay why velocity is not constant because change in Direction axelerate motion okay this type of a question you can expect in your schools got it now so let's move the force that causes acceleration because change in direction of the particle keeps the body moving along a circular path is acting towards the center so if a question asked based on a centripetal force center seing Force okay centripetal force is nothing but a center seeking force center seeking force center seeking of force okay in in your uh School exam they can ask what is the direction of a centripetal force okay what is the direction of centripetal force here the direction acting towards the center okay and example for circular motion okay the first example first example you can consider the motion of a moon around the earth is a due to centripetal force okay if anybody ask you what is the reason moon is always in the circular path around the earth the reason Center seeking Force generally we call it as a centripedal force okay and one more simple example that is a atom if you consider subatomic particle okay so center of the atom we call it as a nucleus and in the nucleus we can see there is a a proton as well as a neutron and the center of the nucleus of an atom is a positively charge due to proton and electron will be revolving around the nucleus of an atom in a circular path and again what is the reason behind it it is a centripetal force got it on the next example okay first example it is done second example centripetal force is provided by the force of attraction by the Earth okay so that centripetal force okay who will provide this that centripetal force between Earth as well as the Moon that is the centripetal force provided by the Earth got it okay right so here you can see the examples other than you know Earth and Moon so first example a spinning a ball on a string so this is uh how the particle of you know or else the path of the ball looks like it is a you know circular path and this hand here the centripetal force provided by the hands of the player okay or else this person acting towards the center of the circular path that centripetal force is it is always acting towards the center of the circular path and here can see a turning of a car okay turning a car next one we can see going through a loop of and roller coaster and here we here here we have one more example the same instead of Moon and Earth here we have consider Moon and sorry Earth and Sun okay not only Earth and Sun here you can consider any other different planets example four uniform circular motion got it okay now let's Mo on to the next topic the topic is universal law of gravitation so first you need to know first you need to know what is a gravitation instead of a you know universal law of a gravitation first we need to know what is a gravitation okay what is a gravitation so here a gravitation means Okay so gravit ation means listen careful okay so if I throw anything up okay let me consider this is a cell okay if I throw upward again it is coming back one more time if I throw upward it is coming back and even these are two bodies okay there is a force between them okay even if I consider this bottle and this pen and there is a force between these two even if I consider the particles of the screen and myself there is a force between them okay so here gravitation is nothing but the force of attraction it is always okay it is always attractive in nature okay universal law of gravitation it is always attractive in nature okay and the force of attraction between any two Mass okay any two Mass we call it as a gravitation got it fine so force of attraction between any two masses even if you consider particle particle has a mass right uh let me consider an example of electron electron has a mass what is the mass of electron that is the 9.1 into 10us 31 K yes of course it is a very small but it has a mass so therefore the force is exist due to a mass we call it as a gravitational force okay the force due to mass is is called a gravitational force and the force of attraction between any two Mass we call it as a gravitation okay so don't be confused between gravitation and gravitational force gravitational force is the due to a mass where uh gravitation is you know the force of attraction between two masses got it fine so here I can write the force of Attraction force of attraction between between between the masses okay between here I'll write one of the very important term attraction between any two Mar masses any two masses is called gravitation okay so here instead of saying any two grav any two masses here I'll consider Earth and mass okay Earth and gravity and gravitation okay so let me differentiate between gravity and gravitation I'm talking about right now gravitation so force of attraction between Earth and any of object okay and what about the gravity what about the gravity what about gravity this gravity this gravity it is also force of attraction the force of attraction or else you can say that force of interaction between okay force of attraction between between any two masses any2 masses okay any2 masses we call it as a a gravity got it and if we consider gravitation it is one reference that is a fixed okay that is the Earth and another body it can be anything it can be pen it can be myself it can be you know a screen it can be a particle it can be Moon it can be a sun it can be you know any other planet or it can be a satellite also but one reference Mass it is a fixed that is the mass mass of the Earth got it so gravitation the force of attraction between Earth and any any object and gravity means it is the force of attraction between any two masses okay so here any any two masses but here it is a fixed Earth and any object got it okay now next one gravitation it is a fixed gravitation means the force of attraction between Earth One reference point it is a fixed and any any other mass of the object okay now statement statement of this universal law of gravitation why do we call it as the universal law of gravitation we are talking about a force right we are talking about a force that means this force force is in unversal why do we call it as a inversal because this Force exist between the bodies are particle which has a mass it can be anything okay so this law is a universal law because it is applicable for any body which is having a mass it doesn't matter about a matter uh sorry size of the body or an object okay body size of the body or size of the object it doesn't matter if it is having a mass then there is a force exist clear now every object in the universe attracts every other object with a force which is proportional to the product of the masses and inversely proportional to the square of the distance between them the forces along the line joining the center of the objects okay so let me consider this is a mass one okay this is the mass one and this is the mass two Mass one and a mass two and according to the statement okay inversal uh law of gravitation so here there is a force exist what type of a force it is the attractive in nature what is that attractive in nature for example this Mass exerting a force on mass two okay this Mass one exerting a force on Mass 2 therefore it is attractive in nature therefore it is trying to bring this body towards it at the same time this mass is also exerting a force on this Mass one and trying to move this body towards it so this is the a force that is attractive in nature okay and we call this Force as you know gravitational force okay so this is f force on a two sorry force on a one due to two and this is a force on a two due to one both are equal in a magnitude okay both are equal in a magnitude but opposite in direction okay both are equal in magnitude but opposite in direction but here we are considering only magnitude of the force that is a gravitational force we are not talking about a direction because already we specified what is the direction of a force existing between uh between a two masses okay so by this the statement what we can write by the statement we can write you know uh the force which is proportional to the product of their mass that means a force okay generally I'm writing f is directly proportional to the product of their masses okay let me write M1 and M2 inversely proportional to the square of the distance okay Force the inversely proportional to the square of the distance let me consider the distance between these two masses is R okay right this is r 1 by r² fine now what I have to do is combine them combine them okay combine them so product of two masses inversely proportional to the square of the distance I want to eliminate this proportional what I can do is consider proportionality constant that is a g M1 M2 / r² so this this this formula is represented by force between two masses okay and here M1 means mass of the body one or mass of the body particle one and here yeah mass of the body two or else mass of the particle two okay or else mass of an object one or mass of an object two and the separation between them that is a r squ okay now so this one we call as a gravitational force okay now so now what is the SI unit of this gravitational force SI unit of this gravitational force okay so that is the Newton again any type of a force having same unit okay that is the Newton and mass one and Mass 2 it is in terms of a kg R it is in terms of a you know meter SI unit okay now here you have a one question sir what is this G what is this G here we are going to deal with the 2 G okay two gs first one small letter g g and the second one that is the capital letter G so that second you know letter G that is the capital letter G what does it indicates so here G indicates Okay g indicates Universal okay Universal okay Universal gravitational constant Universal gravitational constant and the value of this okay experimentally proved the value of this G is 6.67 into 10^ - 11 okay what is the S of this G Newton M Square per kg squ okay and in this particular lecture we are going to consider okay this as approximately 6.7 into 10 power -1 Newton M Square per kg Square okay clear so statement is simple and why do we call it as a universal gravitational constant and this Force okay this force is okay so this force is this force is this force is is independent independent of medium of medium between between the two masses two masses M1 and M2 okay so what exactly this statement indicates okay let's consider there are two masses M1 and M2 and these two masses are kept in a air medium let's assume okay let's assume let's assume example okay let's assume example in air okay in air the force of attraction between these two masses in a air medium let's say that is a 10 Newton okay let's say that is a 10 Newton and the same masses okay so in this case what I have considered so here I have considered separation it is a 1 M okay separation it is a 1 M let's consider whatever the number you know okay this 10 Newton indicates my reference point for example I'm considering after calculation it can be different because it depends on a mass as well as separation between them right so let's assume the separation is a constant and mass of two bodies are constant but condition what I'm considering is first case I have kept these two masses okay in a air medium I got the force of attraction between these two masses is the 10 Newton okay now what happens in case of a liquid in case of a liquid okay liquids let's consider in a in water okay let's consider example water okay if I consider same setup but instead of air I have kept the same setup into the liquid medium that is the water okay same masses and the separation between them is also same the same system I have kept in a water okay then what will be the force your question will be sir will the force will be same or will be different answer is it will remain same okay so still the force between these two still it is a 10 Newton only and let's consider okay let's consider yeah two mediums are enough okay one it is an air and another one it is in a liquid what if I consider okay vacuum in vacuum there is nothing okay there is nothing means even air particles are not present completely empty space okay completely empty space generally in a physic we call it as a a vacuum nothing but space means above our Earth surface in the sky just considered as a sky okay in a sky above the Earth surface above the Earth surface where there is nothing even a air particles are not present in that particular situation also if you consider okay same setup so first case what was the medium that is the air medium what was the force 10 Newton the same setup we have kept in a water that is the liquid medium the force between two masses still it is a 10 Newton on the same setup okay when you take into the space nothing but in a vacuum where there is nothing what is the force of attraction between them means it is still 10 Newton only okay so that indicates this a gravitational force between two masses it remains same okay so that is 10 Newton 10 Newton 10 Newton it is the independent of a medium between two m masses got it okay now why is a universal law why it is a universal law the statement is very very important okay the statement is very very important the statement is simple okay why we call it as a inversal the law is universal in the sense that it is applicable to all the particles all the bodies all the object irrespective of a size and shape if a mass is there then it is applicable okay now it is applicable to all the bodies whether the bodies are big or small whether they are Celestial or terrestrial okay it is applicable between subatomic particles it is applicable between you know micro level it is applicable between any two masses for example let's consider this and this or else this and this whatever it is or else the force between okay force between Earth as well as the moon or else Earth as well as you know sun right it is applicable so that is the reason we call it as a inversal law okay now so let's move on to the this is the mathematical formula that is the gravitational force between two masses okay now so next one importance of this universal law of gravitation what is the so importance about this universal law of gravitation okay the first point you can notice okay the first point you can notice the force that binds us the Earth okay binds us to the Earth okay for example we know that the Earth is in motion around the around the Sun in a circular orbit with a speed lot of speed okay you cannot imagine okay so around 800 something miles per hour okay so just imagine if the Earth is moving that much speed around the Sun why can't we fly away from the surface of Earth we have to fly right for example let's consider Mar go around okay Mar go around so if you leave the support okay you're you know sitting on some toy and it will be moving in a circular path okay you'll be holding some support if you leave that support you'll be flying away like if you uh you know revolving that stone with help of a thread if you leave it what happens it will fly tangentially right in the same way if you go in a mer go round if there is no support what will happen you'll fly away but in the same way on the Earth surface we are not getting any support means we are not holding uh you know any support still we are not flying away we are not flying away from the surface of Earth which one binds us to the surface of Earth or else earth that is a a gravitation that is a force exist between myself as well as the Earth okay so the universal law of gravitation successfully explain several phenomena which we are Bel believed to unconnected initial days we are una unaware of these concept okay unconnected we thought that it is unconnected but later on we got to know this Universal gravitational law successfully explained if we are binds to Earth earth that is the reason simple that is the universal law law of gravitation second one let's consider the motion of the Moon around the earth already we have discussed that is the centripetal force who will provide that centripetal force Earth okay if the moon revolving around the earth then there should be a cental force right who will provide that centripetal force that is provided by Earth only the next one of a planet around the Sun and here so many planets means eight planets okay around the Sun okay moving in a circular path so who will provide centripetal force for all these planets the centripetal force provided by a sun okay and which is explained by inversal law of gravitation and the last one the tides due to the Moon and the Sun so in the sea we can see Tides okay okay so high level and low level okay so Tides what causes that Tides okay so reason it is simple that is a moon okay due to Moon as well as a sun that is the gravitational force bit uh gravitational force due to Sun as well as a moon are the reason for the tides but generally we can say that as compared to the Sun a moon is very near to our Earth surface generally we say that the reason behind these ties it is due to Moon let's consider Moon only okay now so we got to know what is the importance of universal gravitational law then let's move on to the next topic okay next topic that is a questioning part okay so let's uh calculate this question question says example 9.1 uh you know ncrt textbook from the ncrt textbook the mass of the earth is a you know 6 into 10 24 kg okay and that of the moon is 7.4 into 10^ 22 kg if the distance between the Earth and Moon is 3.8 84 into 10^ 5 kilm 5 kilm calculate the force exerted by the Earth on the moon okay that is the centripetal force okay exact by the cental force okay so now G they have considered 6.7 into 10^ - 11 Newton M squ K per kg Square okay by systematic procedure what do we need to follow okay so first we need to write data okay first we need to write down data and what is that given data first one mass of Earth instead of M1 here I have considered mass of the earth that is 6 into 10^ 24 kg fine sir next one M2 mass of the body two that is the 7.4 into 10^ 22 kg that is the mass of the Moon okay let's consider M base M mass of the Moon 7.4 into 10 power 22 kg okay and the next one separation between them okay the distance between the Earth and the moon is 3.84 into 10 power 5 km M okay so what you need to calculate a force between or force exerted on a moon by the Earth okay so F you need to calculate and G they have given okay so First Data we have you know written what is the next check the checking is whether the all the physical quantities are in the same system are different system we have to look it okay now here see mass in a kg SI system yes it is there okay yes SI system yes mass is a measured in terms of a kilogram right yes symbolically kg yes done and what about a distance a distance is nothing but a length what is the as unit of a length that is a meter but here you can see that is a kilometer what you need to do convert that you know into SI unit okay so here I can write this one as 3.84 into 10 power 5 kilometer meter keep it as it is what do you mean by kilo kilo means 10 3 okay so 10 power 3 m now it is in SI unit yes so First Data then check the units then formula what is that formula f is equal to G M1 M2 / r² okay now substitute the values f is equals to what is the G value 6.7 into 10 power - 11 into Mass 1 what is that mass 1 6 into 10 power 24 into Mass 2 how much it is 7.4 into 10^ 22 divided by okay divided by r² where is that r that is the distance is 3.84 into here you can see 10^ 5 10^ 3 it is a 10 Power 8 am I right 10^ 8 bases are same powers can be added or subtracted Ed based on their signs okay now simplification f is equals to okay so let's consider calculator yes see first I'll multiply our numbers okay 6.7 done into 6 done 7.4 done okay so this is 297.00 okay into now so Powers 24 done plus 22 done - 11 okay done it is the 35 10 power 35 okay now so denominator let's check out 3.84 it is a square right therefore into 3.84 yes done it is a 14 point 2 decimal point is enough 14 point 4 into here 10^ 8 double of it 10^ 16 okay now so 2 97.48 divided by 1474 it is a 20 208 two decimal point is enough into 10 power okay already it is a 10 power 35 is there okay 35 if I take this 10^ 16 to the numerator what happens - 16 okay signs becomes a changes okay becomes change if it is a plus it becomes a minus if it is a minus it becomes a plus okay now simplification 35 minus 16 how much it is 19 okay f is equals to okay so 20.18 into 10 power + 19 Newton okay or or you can write in this way also by scientific method so 2.01 into 10^ 20 Newton also both are correct okay both are correct okay so this is the NCI question now let's move on to the next question the question okay force due to gravity okay so force due to gravity anything if you throw okay anything if you throw up after some time it will come down okay anything anything after some time it will come down what is the reason for that so there we know that there there must be a force okay there must be a force but what is the force what is the magnitude of force we have to know okay so here force due to gravity means if you throw anything upward okay upward if let's consider the mass of the body is a 1 kg okay 1 kg if you throw go upward after reaching after reaching a maximum height okay after reaching maximum height what happens that mass of the body comes to the state of rest for a fraction of a second okay for a fraction of a second so then you can consider final velocity is a zero okay so till then we consider and now the first case ignore okay when you throw upward now it is a maximum height okay now it is a maximum height and after reaching maximum height what happens it becomes a you know state of rest for a fraction of second and starts moving downward okay start moving downward so if it is a moving downward what is the force acting on it okay if the apple is falling okay apple is falling what is the magnitude of a force okay what is the magnitude of a force okay what is the magnitude of a force yes of course it is the force acting on it but due to what gravity okay gravity means the force of attraction between two masses one is Earth another one is Apple what is the mass what is the force of that okay so answer is 9.8 Newton sir how do you know that 9.8 Newton by calculations okay how did you do those calculation can you show me those are your answers right I'll show you in the next slides okay so right now what is this force of gravity according to the law of gravitation the Earth attracts every object around it okay towards its Center the force with which the Earth attracts the body is called a force of gravity okay this is the statement you need okay the force with which the Earth attract a body is called a force of gravity and the value of a force due to gravity okay I'll write FG force due to gravity that is equals to 9.8 Newton okay so this is the precise value approximate value for a numerical purpose what we consider 10 Newton okay 10 Newton this is the value okay so value is 9.8 Newton precise value right and here if the object is in a motion means a motion means when a object is moving towards the center of Earth if there is a force acting okay if there is a force acting in the direction of a force what happens to the acceleration or else what happens to the velocity let's imagine if forget about this okay if the body is moving with a certain speed okay let's say 10 m per second if there is a force acting along the direction of a motion of a body what happens to the speed of the body definitely it is going to going to change if there is a change in a speed in a some direction specified Direction then we can call it as a change in a velocity Whenever there is a change in a velocity with respect to time what we call acceleration right so in the same way this apple is a falling down with a sum speed and the force of gravity is acting on the direction of a force sorry in the direction of a motion that means there is a a change CH in a velocity then we can call it as a acceleration if the force is acting due to gravity then what about that acceleration that acceleration we call it as a acceleration due to gravity okay so generally how do you define acceleration it is the rate of change of velocity right how about acceleration due to gravity the acceleration produced in this particular Apple okay due to gravity of earth that is the definition of acceleration due to gravity that's all okay so in the same way acceleration due to gravity a uniform acceleration produced in a freely falling body due to gravitational force of the earth that is the force of gravity is called acceleration due to gravity and here if the person is falling okay if the person is a falling then force due to gravity that is a 9 .8 Newton okay and what about acceleration due to gravity and we know that f is equal to ma a okay F isal to M A and in place of a what we can write f is equal to mg what is this G acceleration due to gravity okay so f is equals to mg okay f is equals to mg and if I consider mass of okay if mass of the body is 1 K okay if I consider mass of the body is 1 K and force due to gravity is equals to acceleration due to gravity okay and we know that this force due to gravity it is that 9.8 right 9.8 9.8 m/ second square is equals to G so therefore here you can consider G value 9.8 m/ second square or okay or approximately 10 m per second Square 10 m/s square what is the condition here we have consider if mass of the body is 1 kg means this apple what is the mass of that Apple 1 kg if I consider here falling object here person it it cannot be 1 kg but let's assume this falling object mass is 1 kg then what will be the acceleration due to gravity precisely it is a 9.8 m/ second second square but approximately you can consider it as a 10 m/ second Square okay right and here you have a question sir what if mass of the body is a different what if mass of the body is different instead of 1 kg it can be any number right do you think this G value going to change okay for such question we have a answer that is value of acceleration due to gravity value of value of acceleration acceleration due to gravity okay that is small letter G and capital letter G already we know that that is a 6.7 into 10^ - 11 Newton M Square per kg right now here according to okay so let's say this is the ground okay nothing but Earth surface let's consider this is Earth surface Earth surface and there is a body okay above the ground above the ground of mass m of mass m okay mass m and mass of the Earth okay mass of the Earth let's say capital letter M mass of the earth that is a capital letter M okay now there is a force of attraction okay there is a force of attraction this is f and this is also F according to universal law of gravitation okay according to inversal law of gravitation here we have f is equals to G M1 M2 ided r² okay so let's consider this is the R square okay this is the R square or else we can consider this is a radius of okay let's consider separation only okay so let's consider this as separation only now if this is the force okay force due to what that is the gravity force due to gravity how do we calculate mass into acceleration due to gravity according to Newton's Second Law we write f is equal to M into a here f is same that is a force due to gravity it is acting downward and mass is same acceleration due to gravity that is a g am I right so I'll replace this F as a mg that equals to G in place of M let's consider mass of the Earth in place of M2 that is the mass of the body divided by in uh what about this one here I do not consider the separation between two masses instead of that radius of the surface I mean radius of the Earth why comparatively okay comparatively separation of the you know Earth surface and object which is having mass m it is very small so instead of considering separation here I'll consider with respect to Center we are considering right center of the earth we are considering okay so let's consider instead of this one okay instead of this one let's consider Earth surface okay Earth surface okay Earth surface and this is the radius radius of Earth okay now so this is the Earth the surface and here you can see the separation from the center of earth right from the center of Earth yes or no Center of Earth we are considering and comparatively the radius of Earth is more than the separation between the two bodies means the surface of Earth and mass of the body so that is the reason we are ignore this so Center of Earth we have to consider okay from here to here we need to consider not from here to here Center of Earth we have to consider okay now so here R square okay this is going to be R squ got it now so finally m m get canceled what about the G value G value it is a g m ided r² so with respect to surface of Earth okay with respect to surface of Earth what is the acceleration due to gravity okay so let's substitute the values okay so let's substitute the values G value we got it GM / r² okay so if G is 6.7 into 10^ - 11 Newton m² per kg squ okay and R is radius okay 6,400 km okay or else 6.4 6.4 here two zos and 6 zos 10^ 6 M okay and mass of Earth mass of Earth it is around uh let me check mass of Earth we have solved one question right mass of Earth is 6 into 10 power 24 okay 6 into 10^ 24 or else here we have a data uh 24 approximately 5.98 they have considered okay so fine that's okay no problem so here Mass here you can consider 6 into 10 power 24 right 24 kg and after substituting all the values in the formula and the final answer that is g value that equals to 9.8 m/ second square and here you can consider it is the independent of a mass okay it is independent it is independent of mass of the body mass of the body mass of the body what does it indicates so mass of the body if I consider this water bottle let's say it is the 1 kg and this is just 5 50 g okay let's consider this is 1 kg and this is a 50 g what is the acceleration due to gravity on these two bodies it remains same okay irrespective of a mass acceleration due to gravity on both the cases or acceleration due to gravity in both the bodies remains the same that is a 9.8 m/s square if there is no air friction okay let's consider if there is no air friction nothing but opposite opposite Force there is nothing that means if I drop these two bodies okay if I drop these two bodies one is a 50 g another one is a 1 kg both the bodies will reach the ground in the same time okay and if I consider one stone and another in of feather okay if I drop both at the same time in the at the same level both the you know substance one is the stone another one is a feather will reach the ground at the same time because it is independent of a mass of the body we know that feather is lighter and stone is heavier comparatively okay if there is no air friction both the bodies reach the ground same time in a same nothing but a same if you drop those two bodies from the same height that is also condition okay both will reach in the same time got it so this is all about acceleration due to gravity force due to gravity and now free fall okay so free fall what do you mean by Free Fall okay this concept is very important for your upcoming classes means class 11th and class 12th okay so here you can see one situation where uh you know one student standing on the top of the hill okay let's consider top of the uh top of the hill and is just dropping means just leaving the object dropping leaving is not throwing okay is not throwing an object just is dropping or leaving the object so leaving or dropping case what happens to the initial velocity initial velocity in this particular case becomes a zero okay initial case initial velocity becomes a zero okay what is the Free Fall let's try to understand okay the falling of a body from a height towards the Earth only under gravitational force of Earth okay with no other forces acting on it means let's consider there is no force acting opposite of the fall of the body okay then we can call it as a free fall but in reality there is a force acting upward that is a air force due to air that we generally call it as a air friction okay so then it is a not a free fall okay so free fall means then there must be no forces acting on it apart from gravitational for Force then we can call it as a free fall okay so the falling of an object or else the falling of a body from a height towards the Earth only under the gravity itational force of Earth with no other forces acting on it is called Free Fall such body is called a freely falling body okay for a freely falling body U becomes a zero okay U becomes a zero that's all this condition is very very important freely falling body what is the velocity it is a zero because you are not throwing just before leaving okay just before leaving what is the velocity it is at rest right it is at rest means velocity is zero if you're throwing means there must be a a velocity but here you are just dropping a a body that means initial velocity zero okay now let's move on to the next concept that is motion of objects under the influence of a gravitational force of the earth okay now here we have some uh equations of motion that we have learned in the last chapter okay last chapter okay that is a uh motion and force and loss of motion we have we had we had us some equations that equations we call it as a equations of motions there are three equations of motion okay the first one if you consider okay the first one if you consider V is equal to U + a the second one yes is equals to U + of a² and third equation of motion v² that is equal to u² + 2 a s okay and the meaning of the symbols here we are using V means a final velocity u means initial velocity and a means acceleration of the body and T is the time taken by the body in a journey okay and what about s s means it is the displacement of the body okay got it now with respect to Free Fall okay with respect to Free Fall with respect to freely falling body what is you that is equals to zero and here you need to consider here one body is dropping okay one body is dropping okay from this point one body is dropping is it visible yes dropping so in this particular situation here you can write U is zero and this is the G value acceleration due to gravity acceleration is produced okay acceleration is produced in this ball so that we can see in a equal interval of time the distance is covering is unequal that means there is a nonuniform motion Whenever there is a non-uniform motion definitely there is a change in velocity Whenever there is a change in velocity we can call it as the acceleration but due to what that is due to gravity so that acceleration is a due to gravity therefore simply we can call it as a acceleration due to gravity okay now so motion as well as the force due to gravity in the same direction therefore in a downward Direction okay so here very important point in a in a downward Direction in a downward Direction in downward Direction in downward Direction okay a becomes positive G and in upward Direction upward Direction upward Direction a becomes a minus what is the reason the force of force due to gravity acting downward and if the vertically moving object okay if the object is moving vertically motion as well as a a force or else you can say velocity as well as acceleration due to gravity are opposite therefore negative sign if velocity and acceleration if they are in a same direction you can consider a positive example here the motion of the particle and acceleration due to gravity this is a a motion that is nothing but a velocity okay this is the velocity and acceleration both are in a same direction therefore G is a positive what if G is always vertically downward because that is a due to gravity what is the direction of acceleration due to gravity it is vertically downward what if the object is moving up in this particular case object is moving up in this particular case and here you can see acceleration due to gravity is moving downward both are opposite therefore here G that means a becomes okay a becomes minus G and in this case a becomes plus G that's all motion of the body and acceleration due to gravity if they are in the same direction G value positive okay and if motion of the body and acceleration due to gravity opposite means that is a negative here I have written okay now compare the equations okay and for a free fall here we have consider U is equal to 0 right first equation of motion so V is equal to u+ okay u+ and what happens to the first equation u z right U is zero according to the condition a means it is a downward motion therefore g t therefore I can write V is equal to GT okay right first equation done comparing okay now second equation second equation yes but here instead of s we are considering height of the body okay height of the body from here to here okay height of the body we are covering with a H with a h okay height of the body now H is equals to okay H is equals to 0 into t plus of as it is a in place of a the motion is downward therefore plus g into d s t² okay 0 into T it is still zero off GT sare okay height that is of G t² Fine second equation of motion is also done okay second equation of motion is also done and the final one okay so final one that is a v² + 0 S + 2 + g into yes in place of s that is a h okay so v² that is equals to 2 g h clear okay so these three equations are very very important okay uh they can in your school they can ask for your unit test midterm Preparatory okay and Final exam also so this is how you can rewrite motion of an object under the influence of a gravitational force of the earth got it okay now let's uh move on to the next concept huh question a car Falls of edge okay it is a Edge Edge Ed Edge okay Edge and drops to the ground in a 0.5 second okay 0.5 second let G equal to 10 m/s squ for simplifying the calculation sir why we have considered 10 m/s square actually G value is 9.8 m/s square but why we have considered 10 m/s square the reason for a simplifying calculations okay simplifying calculations okay the first one first one okay so first write down data so according to the data according to the data so what is the data they have given time how much it is 0.5 seconds and G value 10 m/ second Square okay both are in SI unit fine and here one more data they have given in terms of a wordings okay in terms of a word word that is a false okay false means initial velocity is zero okay initial velocity zero fine the first question first question what is the what is its speed on a striking the ground okay so on striking the ground means which equation of motion we have to use here we have a total three equations of motion right V is equal to U + e t and the second one s is equal to U + r² okay and the next one last one v² is equal to uh U ² + 2 GH or else directly you can write v² = to U ² + 2 a s and here we need to calculate its speed on a striking the ground final velocity you need to calculate okay and if you want to calculate a final velocity here we have a two equations okay two equations what are those so first one V is equal to GT from the pre equation and second one v² is equal to 2 GH okay from these equations which equation of motion you have to use GT and 2 G which equation so in the data if you see properly there is no information of a height right therefore you have to go with this formula the first Formula okay so therefore here the first one okay so V is equals to GT so after substituting the values G is a 10 and a time that is a 0.5 second okay so V is equal to 5 m/ Second so this is the velocity of a car which is striking the ground okay the next one second uh this is the velocity yeah second one what is its average speed average speed during the time that is 0.5 seconds okay average speed average speed means what is the formula for that average speed okay here I'll write V average speed here I can write initial velocity plus final velocity divided by 2 this is the average velocity that we have learned in the motion in a straight line okay and substituting the values okay substituting the values we average that equals to initial velocity how much it is initial velocity zero yes and the final velocity is a 5 divided by 2 and V equals to 5 divided by two so finally you can write okay V average right this is the V average not V it is V average that is 5 by 2 and V average that equals to 2.5 m/s so this is the average veloc velocity okay of the car now last one how high is the ledge okay ledge it is the correct only okay this is correct only ledge means height of the you know uh car which is a falling and how high is the ledge from the ground third third point that is the third sub question height here you need to find out which equation of motion you have to use okay so here we have a here we cannot see H value here you can see H value here also you can see H value any one of the two equation you can use okay I'm using this one okay that is H is equal to half GT s okay so H is equal to F GT ² fine substituting the values of into G Val is a 10 and time is 0.5 into 0.5 okay so here to eliminate this what I have considered is 10 into 0.5 that is a 5 into 0.5 divided by 2 okay now here to eliminate this 0.5 what I'll do multiply and divide by 10 okay multiplied and divide by 10 now finally H is equals to and here you can see 5 into 5 divided by 2 into 10 that is the 20 and 25 divided by 20 20 and 5 5 is 25 and 5 4 is 20 so 5 by 4 okay so 5 by 4 means it is approximately 1.25 M height the height of the ledge is 1 25 M okay that is a 5 by 4 value 1.25 M okay got it now let's come on to the next question next question an object is a throne not fall okay it is a throne it is a throne vertically up vertically up and raises to the height 10 m calculate the velocity with which the object was thrown upward and the time taken by the object to reach the highest point okay so let's try to understand the given question with the diagram okay so this is the ground this is the ground and from the ground okay object is a projected object is projected okay object is projected fine object is projected with a initial velocity U okay initial velocity U but you don't know what is the initial velocity and what happens it will travel some height at maximum height okay top Point okay top Point top point what happens to the velocity it comes to the rest that means the final velocity is zero okay now vertically upward okay vertical upward so acceleration due to gravity it is always acting downward right acceleration due to gravity always act downward now you see velocity or motion of the object acceleration to the gravity opposite in direction therefore what happens to the G value that is a minus G okay therefore from the diagram you can notice you have a V value you have a you don't have a u value but you have a v value and a value okay and a g value you can considered as a 9.8 m/s Square it is a known parameter right now first question what they've asked the velocity with Which object was thrown this one so here you can see it is a independent of a time right it is the independent of a time and also if you see the data clearly from this point to this point okay from this point to this point height okay that is a 10 m 10 m that is a height okay now you have height but it is just independent of time which equation of motion you have to use okay which equation of motion you have to use in entire data it is independent of time therefore you have to use third equation of motion okay third equation of motion third equation of motion that is v² is = u² Plus 2 a s okay now substitute substituting the values okay substituting the values V value at a top Point what is the value that is a 0 whole square and you don't know U therefore U Square as it is + 2 and what is the value of a it is a is a negative negative G and in place of s that is a h only okay so it is a 0 square it is a zero only U S Plus into minus minus 2 into 9.8 into height is a 10 okay and what I'll do I'll you know rearrange this equation what I will get u² that is equals to and 2 into 98 okay 2 into 98 2 into 98 let's calculate this one 98 into 2 196 okay u² is equal to 196 okay and if I Want U I have to take under root 186 okay now U is equals to uh this is 196 let's check out for under square root of 16 okay so 96 and six and one okay six and this is 6 and one and this is 50 and this is 2 256 that means the 16 is not possible okay 16 is not possible okay so let's check out one more time huh okay directly we can use uh [Music] calculator so first so first 2 into 9.8 into 10 196 under square root 14 okay so the value is 14 14 m/ second okay so the value of initial velocity 14 m/s okay the first uh sub question it is a clear now second Point what they're asking the time taken by the object to reach the highest point this is the highest point or top Point okay so here which type of equation of motion we have to use the first equation of motion okay first equation of motion and this one also you can use no problem wherever there is T you can use okay so by the data you can use this one or you can use this one Whatever you want you can use this okay so here of second equation of motion you have to use why not this final velocity becomes zero so T becomes a zero okay so maximum height we are we are going to calculate okay initial velocity we have okay fine yes by the data you have you don't know initial velocity okay initial velocity okay already we calculated right so by that also you can calculate so what is the value of H is equals to of GT squ okay GT Square so after rearranging this okay 2 h / G so what is the value 2 into 10 / 9 .8 so that is a 20 divid 9.8 okay so 20 divid 9.8 that is 2. t² is equal to 2.04 okay this is enough and T is under square root 2.04 here plus or minus signs will come but let's consider a positive only okay because the time cannot be negative and the time is T is 1.42 seconds okay this is the required solution okay fine only two sub questions let's Mo on to the next question Mass what is this Mass what is this Mass here we have I guess mass as well as you know Mass after that here we have a weight of the body also okay weight of the body so first try to understand what is the mass mass is is it is the property of a body okay it do not change why because if you consider any substance okay any substance it is made up of a matter so if you consider a body or object the amount of matter contained by the object is called matter so that matter if you place on the surface of Earth if you place on the surface of moon if you place anywhere the amount of matter contained by the body Remains the Same okay so mass is nothing but it is the amount of matter contained by the body okay so that is the mass okay right the amount of matter contained by the object or body is called mass of the object and in the second chapter force and loss of motion when we are talking about inertia what is the measure of inertia mass is the measure of inertia we have discussed about it okay so mass of the object is the measure of its inertia okay mass of the object object is measure of its inertia fine second one how do you measure a mass by using beam balance or a physical balance okay and what is the unit of a mass already you know that that is a kilogram right so SI unit is a kilogram SI unit is a kilogram and symbolically we can represent as a small letter kg and quantity whether it is is a scalar Co or vector Co it is a scalar only because we are not talking about any direction of the you know body just we are talking about amount of matter contained by the body okay so amount of matter contained by the body let's consider this is the one body and this is the second body okay so amount of matter contained by the body if I take these two bodies and keep on the beam balance okay based on amount of matter of the body contained by these two okay amount of the matter contained by this and this okay it will show by reading okay so that beam balance or physical balance so by appearance you can notice this the amount of matter contained by this body is more compared to this I hope you know that what is the matter in chemistry I hope you have already learned about what is matter okay matter is nothing but something which is occupied by space and has a mass and pursued by our senses okay so this nothing but you know matter only but how to define a mass mass is nothing but amount of matter contained by the body that's all okay right next one measuring device measuring device you can consider a beam balance okay that one beam balance beam balance or physical balance physical physical balance okay and here our question is mass of the object is constant or variable variable means it changes do you think the mass of the body changes yes okay but here under certain conditions okay under certain conditions what are those if the speed of the object is less than speed of a light what is the speed of light here if it is the okay here I'm considering less than speed of speed of light here condition I'm applying if less than speed of light that is C is equals to that is C indicates speed of light okay 3 lakh kilm per second okay 3 into 10^ 8 m/s if it is less than the speed the mass of a body constant do not change okay here you can see mass of the body is constant mass of the body is constant okay if you take any body which is having a mass it will remain same okay for example let's say mass of this object okay mass of this object say it is a 1 kg on the surface of Earth and this mass of the body taken into the surface of a mo still its mass remains same because it's just amount of matter contained by the body or any other planet or any other satellite or any place in the universe the mass of this object remains same okay uh and your condition is if the speed of the body is less than you know speed of light or else you can say in simple word okay constant at rest okay constant at rest constant at rest okay constant at rest and what about Sir what if this speed of the body is moving with more than speed of light it is not possible if so the mass of the body going to be changed under relative St mechanics okay so that is given by m not idun 1 - v² / c² now at this position in n9th class it is not required at rest yes mass of the object is a constant it is not going to change maybe it is on the surface of Earth maybe it is on the surface of moon or anywhere in the universe got it okay this is the condition at rest now let's move on to the next concept that is the weight okay that is the weight what is this weight if there is a mass of the body okay on the surface of Earth okay if I leave it what happens it will come down what is the reason behind it that is the force due to gravity that's all and this force acting on the mass of of the body it is given by mass into acceleration due to gravity okay so by the concept okay according to newtons a second law what do we say f is directly proportional to the m into a here Mass let's consider mass is a constant okay mass is constant or else here in place of acceleration here we are considering acceleration due to gravity so if there is a mass okay on the surface of Earth if there is a mass on the surface of Earth there is a force acting on the body it is always vertically downward so that we call it as a weight of the body and this weight of the body is nothing but weight of the body is nothing but the force by which Earth attracts towards the center of Earth okay it is simple okay weight is nothing but a force okay with which the force of gravity or else force due to Earth is attracted towards the Earth surface that's all okay and the force it is the given by okay force it is given by m into G simple okay M into G clear the same formula this is a mass got it now so according to the definition let's read out once the weight of an object is the force with which it is attracted towards the Earth that we call it as a weight of the body and this weight of the body depends on acceleration due to gravity and acceleration due to gravity depends on mass of the planet and radius of the planet for example here uh on the surface of Earth the G value is 9.8 m/s Square what is the reason G is a constant that is a capital letter G is a constant and mass of the Earth and radius of Earth are Dependable parameters okay if M as well as R changes what happens to the small letter G that is also changes getting my point okay and here I want to say this okay capital letter G it is a constant okay it is a constant what is the value of this that is a 6.7 into 10 power - 11 Newton m² per kg squ okay it is remain same wherever it is okay wherever it is maybe on the surface of Earth maybe on the surface of moon maybe on other planet anywhere in the universe but second one okay second one this small letter G small letter G that is not a constant okay it is a variable it is a variable it is a variable okay why because this G depends on g m / R this m indicates mass of the planet okay here I have consider okay if I consider acceleration due to gravity on Earth that means this G is a constant and mass of the earth divided by radius of Earth okay what if I consider a moon acceleration due to gravity on the moon surface G is a constant and here mass of the Moon divided by okay mass of the moon divided by radius of the Moon okay so as mass as well as radius changes this g g value is also going to be changed getting my point on the surface of Earth that is 9.8 m/s square but the same acceleration du to gravity if I consider on the surface of a moon that will be different because it is depends on you know mass of the planet or mass of the location and radius of that location getting my point okay simple now next one next one so definition is clear weight is nothing but a force only okay weight is nothing but a force only weight is nothing but a force okay due to gravity okay of the planet okay now SI unit if it is a force what is the SI unit of a force that is the Newton and it represent by capital letter n and quantity it is the vector quantity because it is always always acting towards the center of Earth or center of the planet as we are talking about you know Earth here I'm talking about a center of Earth okay vector quantity because it is always directed towards the center of Earth see direction towards the center of Earth now measuring device weight is measured by okay weighing maion or else you know uh spring balance okay force is measured by okay force is measured by force is measured by spring balance okay spring balance this is the spring balance okay spring balance spring balance this is a weighing Mission this is weight weight is measured by a weighing Mission but this weighing mission is Works based on a principle okay spring balance only okay weighing Mission Works based on a principle spring balance only therefore directly you can say this weight of the body is also measured using a spring balance okay if you don't remember in your in your examination all just write down it is a weighing maion that's all okay because weighing machion Works based on the principle that is the spring balance got it now device spring balance or weighing mission okay done next one relation between the mass and weight of the body already we have derived that is weight of the body that is equals to mass here I'll WR weight of the body weight of the body that equals to mass of the body and acceleration du to gravity acceleration due to gravity acceleration due to gravity here we can consider W is equals to mass into acceleration gravity that is mg okay I hope it is a clear for everybody now next one that is weight of an object on the moon here we have have you know two situations means two locations one is Earth and another one is a moon and here we need to calculate what is the weight on a surface of Earth and what is the weight on surface of a moon of the body okay so let's consider here just we need to find out you know weight ratio of the weights okay ratio of the weights ratio of the weights okay now so let's consider this is the first case yes same body and this is uh let's consider this is Earth surface and this is the moon surface okay now this is Earth it is not visible Earth surface and this is a moon okay now so this is mass of the body and this is also mass of the body and we know that force is always acting towards the center of the you know Planet here I have considered Earth and here I have considered Moon okay now so here we need to calculate the ratio of weight okay so therefore here what I can write weight of the body on Earth surface that is the we that equals to mass of the body okay mass of the body or else you can write weight of the body is nothing but a force that is on Earth and here weight of the body on a moon that is nothing but a force on a moon okay now consider a force Universal gravity gra itational law according to Universal gravitational law this F is equals to F generally okay f is equals to G M1 M2 / r² okay so here I'll consider so w e that is the weight on the surface is equals to substitute the same formula that is a g M1 means here mass of the Earth I'll consider mass of the earth into Mass of the body divided by radius of Earth Square okay in this case weight of the body and the Moon that is equals to G is a constant mass of the Moon mass of the body divided by radius of the Moon Square okay now take the ratio we e divided WM that is g mass of the Earth mass of the body okay I'll write a b and here also B mass of the body as a b MB okay and divided by radius of Earth Square okay into weight of the body weight of the body on the moon surface that is g mass of the Moon mass of the body and radius of the Moon Square okay now here you can see G and G get cancel and mass of the body and mass of the body get cancel and remaining you can see mass of the earth into radius of the Moon Square divided by mass of the Moon divided into radius of Earth Square okay clear now what do you have to do so weight of the body on a surface of Earth divided by weight of the body on surface of a moon that equals to so Mass compare that me id mm me id mm grouping Mass with mass and radius with radius okay and RM divid R RM ided r e whole Square now substitute the values we e divid WM mass of Earth how much it is here 5.98 into 10^ 24 5.98 into 10 power 24 kg divided by this one mass of the Moon that is 7.36 7 7.36 into 10 power 22 I guess let me cross Check Yes 22 only and radius of Earth okay so radius of Earth so that is 6.37 into 10^ 6 6.37 into 10^ 6 divided by radius of the Moon that is 1.74 1.74 into 10^ 6 whole Square okay and here you can see so 10^ 24 and 10^ 22 here two remaining and 10^ 6 10^ 6 canceled out so we e ID WM that equals to that equals to take the calculator for easy calculations see 5.98 divided by 7.36 5.98 divided 7. 36 that is uh you know 0.8125 into 10^ 2 is left out therefore 100 into 100 so that is is 8125 okay into this one so 6.37 divided by 1.74 okay so this is the value so that is 3.66 whole Square okay so now huh ratio we have to calculate right H okay fine that's fine so here you can write 3.6 into 3 okay 3.66 3.66 into 3.66 into 8125 that is 10 88 one 88 okay 10 88 39 okay or else you can uh further simplify this one as you know 5.6 this is 5.98 as 6 and 7.36 as a 7.35 okay so this is one way of writing okay weight of Earth that is 10 18839 times of weight of the body on a moon this is one way okay this is one way or else so consider from here only okay consider from here only okay so weight of the Earth okay weight of the Earth and uh weight of the Moon okay and here we have another way that is f w is equals to mg okay mg so here you can write that as okay weight of the uh G value okay so here m m g e divided W is equal to m g m okay m m get cancel so here G mass of the earth divided by r² E and here g m Moon divided by R m² okay and again simplification this is R okay R method and M that equals to okay now so g g get cancel mass of the earth divided radius e squ okay r e s into R m² divid mass of the Moon okay so after simplification okay after substituting the values and everything okay you will be getting 1X 6 1X 6 WM got it okay clear that indicates that indicates acceleration due to gravity on a moon that is equals to 1x 6 times of acceler acceleration due to gravity of body on Earth or else directly GM is equals to G ID 6 okay so these are simply simple calcul AR can do it okay and here here also you can write this one as okay so this one as so we e divided by uh reciprocal also you can write so this becomes 1 by 6 or else W divided by 6 okay now let's move on to the next concept that is question 9.4 mass of an object is the 10 kg what is its weight on a earth simple question okay so data if you write a data if you write data okay so here mass that is a 10 kg and on Earth they have asked that is w and we know that we that is equals to GM or mg right m g that is acceleration due to gravity on Earth so we is equals to mass that is a 10 kg into this is a 9.8 right so w is equal to 98 Newton 98 Newton got it simple calculations nothing to worry got it now next one an object weighs 10 Newton when measured on the surface of Earth what would be its weight when measured on the surface of the Moon already we to know first write write down the data then we'll proceed how to solve this approach okay what is the approach of solving this question so first they have given object weight on the surface of Earth that is weight of the Earth weight of the body and Earth surface that is 10 Newton okay and what would be its weight when measured on the surface of the Moon weight of the body on the moon surface question mark so by the data You can conclude that okay we is equals to okay and uh mg okay and we value we know that that is the 10 is equals to mass how much it is mass we have to calculate and G that is a 9.8 okay M value that is given by 10 / 9.8 kg okay right this is the mass of the body now here we need to calculate weight of the body on a moon surface okay and here we can write mass of the body into acceleration due to gravity on moon surface and we know that acceleration due to gravity on moon surface that is 1 16 time of acceleration due to gravity on surface of Earth substitute the values okay so w m that is equals to M value that is 10.98 okay and GM GM value we know that that is 1.1x 6 into G Okay g and we know that acceleration due to gravity on Earth's surface 10 / 9.8 into 1X 6 into 9.8 okay so here 9.8 9.8 get cancel so we that is equals to sorry this is a WM not e weight of the body and the moon so 10 by 6 so for 10 by 6 what will be the answer 10x 6 that is 1.66 1.66 Newton okay simple okay there is one more method okay RS we can solve it how sir one more method method two method two direct method okay method two so weight of the body on a moon surface that is equals to mass of the body okay into acceleration due to gravity on a moon surface okay now so here they have a given this one 10 okay and we know that weight of a body and a moon surface that is equals to weight of the body on Earth surface divided by six that's all okay so Moon that is equals to so weight of the body on a moon earth that is 10 divided by 6 that is 1.3 sorry 1.66 Newton two steps only only two steps okay when you know the relations Aram you can do it okay when you know the relations Aram say you can do it okay no problem fine next one that is the thrust thrust to topic so like weight weight is the type of a force okay weight is nothing but a force by which okay which attracts towards the center of Earth nothing but we can say that a force is nothing but a force only thrust is also Force but what kind of force that we need to know okay Force force is a vector quantity it can be applied in any direction right any direction on the surface okay so let me consider let me consider this is the surface of Earth okay or else any surface okay so I can apply a force in this way with respect to uh normal okay and this way right or else this way okay or else this way or else you know this way all right this way and this way also okay so here you see all these are a forces okay this is also Force this is also Force this is also Force this is also force and this is also force with respect to normal okay normal means perpendicular to the surface perpendicular to the surface okay perpendicular to the surface perpendicular to the surface from point of contact point of a contact this is also a normal okay now here I'll give the name this is a one and this is a two and this is a three and this is a four and this is a five out of five okay all these five are are forces only but in five cases there are two forces are a Thrust thrust means a force acting on a Surface normally or else perpendicular to the surface okay perpendicular means for example if you consider this one here there is a angle Theta but here the angle is 90° here angle is 90° here there is a angle Theta and here there is the angle Theta means 1 and four and five are forces forces with angle with the angle Theta and two and three forces with angle with the angle 90° or normal or perpendicular okay all the terms are same perpendicular perpendicular okay so this two and three cases only we are calling it as a Thrust we are calling it as a Thrust nothing but when a force acting on a Surface normally or else perpendicular to the surface or else with angle 90° with respect to the surface so those forces only we are calling it as a Thrust okay thrust is nothing but again I'm telling you it is the type of force okay right so we got to know what is the thrust okay thrust is a normal force which is acting on the surface already we have seen the examples now s unit as a Thrust is the un uh thrust is the force type of a force means what is the s unit it is a Newton okay and the quantity it is a vector quantity because it has a direction also because normal to the surface okay now next one a pressure pressure means it is the RTI of a Thrust and area or as we can call it as a you know thrust per unit area we call it as a pressure okay simple now in this particular case Okay in this particular case let me consider this is the surface and here there is a force acting okay there is a force acting with a 90° so this is the thrust yes of course this is the thrust and what is this this is the area this is the area one more example let's consider let's consider this is the surface okay and this is the force this is the force okay this is the force this is the the force acting on the surface okay this is the force acting on the surface but what is the area this much so this is the area Okay area and this is the force acting on the surface this is the force acting on the surface so this is the force okay so that is nothing but a Thrust with respect to surface it is a 90° only so the thrust per unit area we call it as a pressure okay okay thrust per unit area we call it as a pressure got it now thrust per unit area we call it as a pressure simple now formula wise pressure that is equals to thrust per unit area so generally okay generally in textbook they'll give you f ided 8 but actually it is the thrust per unit area not just force per unit area Force per unit area it is not the right answer but precisely okay that is generally correct but precisely pressure is nothing but a Thrust po unit area got it now next one SI unit if you look at the you know formula unit of a pressure that is equals to Newton per M Square what is the unit of area that is a meter Square so here this Newton per me Square only we call it as a pascal we call it as a pascal so represented by PA so here also same Pascal or okay I'll write a full words only Pascal that is given by PA or 1 Pascal that equals to 1 Newton per M Square okay both are correct clear and quantity it is a scalar only okay and a measuring device barometer barometer this one is a barometer okay got it now next one questioning part 9.6 a block of wood is kept on a tabletop the mass of wooden block is is a 5 kg Mass they have given okay 5 kg mass and its dimensions are 40 cm into 20 cm into 10 cm nothing but they are talking about length into breadth into height okay so length into breadth into height nothing but they have given volume find the pressure find the pressure exerted by the wooden block on the tabletop if it is a made to lie on the table toop with its sides of a Dimensions here we have two situations where area is a different okay the body is same but area is different okay now so first one data we need to calculate I mean first we need to write down data data okay done data it is completed so they have given volume that is uh 40 cm okay okay 20 cm okay 10 cm fine find the pressure pressure we need to calculate okay so here we have a two situations for area first case that is a 20 cm into 10 cm and the second case area because length into bread nothing but area only right so area is nothing but length into breadth okay but they have given here length this is the breadth and this is the length and this is the breadth okay next case that is a 40 cm into 20 cm okay fine so here pressure so pressure means pressure is nothing but a Thrust or else a force perpendicular Force divided by area so force is given by okay force is given by mg nothing but weight of the body force is nothing but here we are talking about a weight divided by area and weight it is given by mg divided by area Okay area of crosssection I mean area of the you know block which is covered or occupied now so let me consider first case Okay so first let me consider uh weight of the body mass that is a 5 kg into G value that is a 9.8 okay 9.8 acceleration new to gravity 9.8 so w is equals to okay so w is equal to 5 into 9.8 49 49 Newton that is nothing but a force I'm considering Force okay right so here we need to calculate uh you know area for this okay first case right so now area that is given by 20 cm centimet means first we need to consider into meter cm to M that is nothing but 20 10 power - 2 m into 10 into 10^ - 2 m okay now so already we know that pressure itate is given by force divided by area substitute the values pressure that is equals to 49 Newton divided by area area how much it is 20 see first I'll substitute the values here I have done this one so so here so 20 into 10 that is the 200 so 200 into 10 power - 4 okay so let me write 200 into 10 power - 4 fine so pressure is equals to 49 okay 49 divided by this one can be written as 10^ 2 because this two zeros can be written as a 10^ + 2 into 10 power minus 4 okay so 49 divided 49 49 divided by 2 that is 24 okay so 49 divided by 2 it is nothing but 24.5 into 10 power 2 okay 10 power 2 so finally you can write pressure that equals to 2 2 450 Pascal or 2 450 Newton per M squ okay so if you have any question in this step so what happens 10^ 2 10^ minus 2 what happens here here let me write this one pressure is equal to 49 / 2 into 10^ -2 okay if if I shift that into numerator it becomes a positive okay plus two got it now second case second case we have to solve so second case that is given by pressure is equals to 49 / area so first let me write area only so area second case area that is 4020 so 40 into 20 40 cm into 20 cm it is in CGS unit let me consider into SI unit so 10 power - 2 m into 20 into 10 power -2 M okay so area so 40 into 20 40 into 20 that is 800 into 10^ -4 M squ okay and after simplifying this this can be written has 10^ 2 8 into 10^ 2 into 10^ - 4 M squ so finally you can write a is equals to area is equal to 10^ - 2 m squ now pressure now pressure so pressure is equals to so pressure is equals to force already we got it 49 divided area that is 8 into 10^ -2 okay so 49 divided by so 8 that is uh 6.125 into 10 power + 2 because when you shift this 10^ minus 2 from denominator to numerator it becomes a positive okay so after simplifying this into 100 this becomes pressure that is equals to 61 2.5 Pascal or 61 2.5 Newton per M Square okay so that's all two cases they have asked two cases we have solved this one okay now let's move on to the next concept that is the pressure in a fluids okay so first case Okay pressure in a solids why there is a pressure in a solids at a contact okay so where does the pressure exerts in a solids the pressure will be exerted between the contact between two surfaces okay that is due to weight of the body okay a simple statement okay regarding uh solids the pressure due to solids is due to weight of the solids or else a body now in the same way the pressure in a fluids that is also due to weight of the fluids so first question sir what do you mean by fluids fluids means the substance which can flow the substance which can flow example so uh liquids and gases okay liquids let's consider a water water can flow consider a gas State example that is the air air also can flow so that means combination if you consider liquids as well as a gas we can call it as a fluids okay and these gases as well as a fluids nothing but a liquids have a weight therefore liquids as well as a gases also exert a pressure but in all the direction in all the direction the liquids or fluids exert of pressure but in case of a solids okay in case of a solids the pressure is exerted only at the bottom in which they are in a contact okay only at the bottom or else the place where the objects are in contact so that is the only place the pressure exerted by the solids but in case of fluids they can exert in all the directions okay in all the direction see all the liquids and gases are a fluids okay this statement is very important what are the fluids fluids the substance which can flow the substances which can flow a solids exert a pressure on the surface due to its weight similarly fluids have a weight and they also exert a pressure on the base and walls of the container in which they are enclosed pressure exerted in any confined mass of the fu is transmitted and diminished in all the direction means in all the direction the pressure will be same okay pressure will be same in case of a fluids got it now next case uh biony and weight of the body Okay so these two terms are very very important first all let's already we know that what is weight weight of the body is nothing but a force by which you know Earth attracts towards it okay so that is the weight of the body and what is the you know benefit of that weight what is the you know uh weight to do weight of the body has a tenden okay weight of the body has a tendency to sink the a body to the bottom of a liquid huh what is this sir let's consider example let's consider with example okay so this is the container okay let's consider a container and here water here water let's consider uh one more object object okay so it has a weight it has a weight okay it has a weight because of the mass okay because of the mass so this weight what does it do is it has a tendency to sink the body to the bottom means this one can sink the body to the bottom so this is the final state of the body means place of the body so weight of the body has a tendency to syn the body see weight of the object weight of the object is the force with which it is attracted towards the Earth it has a tendency to sink the body in our liquids okay when we kept a body in the liquid it has a tendency to sink the body to the bottom of a liquid but what about you know what about a biony this biony is also type of a force see weight is also type of a force thrust is also type of a force and here Bion is also type of a force but it is a due to fluids okay let me consider example of a uh air okay air is a fluid okay so when you take a paper and just throw it it do not come directly on the floor okay it do not come to the you know or else do not reach the ground directly first what will happen it will be floating after some time it will come to the ground so why it is happening because the force due to air it is exerting in vertical upward okay vertical upward in the same way let me consider a water bottle okay so first what you have to do first you have to empty this water bucket uh water bottle okay first you have to empty this water bottle then what you have to do you have to you know uh put this cap and uh you have to take it there should not be any Gap means air should not enter okay so first you have to keep it very tight and what do you have to do next so take this water bottle and try to push inside the liquid okay so due to your you know Force applied force due to your hand it will move inside the water okay try to push it down means to the bottom okay and after some time when the water bottle in the inside the liquid okay remove our hands what happen this water bottle will be coming upward yes or no okay try to push it again again again it will come up why what is happening the reason simple the liquid is also exerting a force in a vertically upward Direction okay the force exerted by the liquid is called a bon or else force of bony okay and it has a tendency to move the body up okay to move the body up got it now so beon C is the type of force okay again I'm telling you you bance is the type of force the force exalted by the liquid in the direction vertically up vertically upward but weight of the body towards the center means has the tendency to sink the body in the liquid it has a tendency to move the body upward got it okay so that means based on okay based on weight of the body and bany force of a liquid okay FB F Bas B bany bancy force of a liquid okay force of a bony okay relation between these two will give you whether the body or sink to the bottom or float on the surface or submerged between the Surface and liquid okay shall we see that special cases yes the first case why object float or sync when placed on the surface of water so reason relation of Bindy Force and weight of the body okay weight of the body it is given by mg Bion force of the liquid it is given by row v g means this a force of bons is also depends on some parameter those are density of a liquid okay here I'll write density of a liquid density of a liquid density of a liquid and V is the volume of the liquid sorry volume of the the body okay volume of the body and G is already we know that acceleration due to gravity acceleration due to gravity due to gravity okay B is the force exerted by the liquid in the direction vertically upwards it has a tendency to move the body upwards it is given by row VG okay next the weight of a object weight is nothing but it is a force okay acting on object force with which it is attracted towards the Earth it has a tendency to syn the body in the liquid in the liquid okay now let's see the special cases the first one okay first case first case the weight of the body that is W is greater than bind force of the liquid okay so when weight of the body is greater than bive force of the liquid greater than ban force of the liquid so initially what I'll do I'll take the body I'll take the body okay round shape only it's up to you okay whatever shape you want you can take no problem okay now let's consider this is the body okay this is the body and due to weight okay on this body there will be two forces are acting one is weight of the body okay another one is bind force of the liquid okay this is a bind force of the liquid and this is weight of the body when you keep an object when you keep an object on the surface of the water or else a liquid let me consider surface of the liquid only water example water only I will consider okay so what happens is for this condition as weight of the body is a more what happens it will move downward because it has you know more tendency so therefore what happens to the body it will move downward in Direction therefore finally the finally the body will sink finally the body will sink the finally body is at bottom at bottom okay so here the condition what happens body syn okay right next case next case if the weight of the body is equal to the B Force means bind force and weight of the body are equal again I'll consider same a body okay same body on the surface of the liquid and we know that there are two forces are acting okay there are two forces are acting one is acting downward another one is acting upward and if you consider this is weight of the body and this is a bind force of the liquid and what will happen is this body will be submerged submerged means just inside the water inside the water surface okay just inside the water surface okay just inside the water surface so here you can see weight of the body is still acting downward and B force of the liquid moving upward FB and weight of the body okay so here body submerged submerged means it is cannot be floating on the surface of water okay and it cannot be sink to the bottom means between okay just below the surface of water it is floating it is not a sinking are completely floating it is the submerged means just below the surface of water it is a submerged okay what happens if weight of the body okay if weight of the body is less than bind force of the liquid okay bind force of the liquid okay bind force of the liquid let's consider so this is the body okay this is the body and uh and again on this there are two forces are acting one is upward Force another one is downward Force downward Force we call it as a weight of the body and upward Force we call it as a bind force of the liquid okay now so here you can see it is a floating floating okay it is a floating based on okay based on volume of the body and density of the liquid the submerged part will be decided okay submerged part will be decided so here weight of the body and bind force of the liquid in this case weight of the body is less than bind force of the liquid okay so it will be floating floating okay the body will be floating simple and this floating and sinking concept can be uh you know explained with the help of a density also density of a body and a liquid So based on that also we can explain the body sinks or floats okay right now we are explaining with respect to weight of the body and bind force of the liquid got it now Archimedes principle statement is very very important Archimedes principle statement is very very important the statement is simple you know second second case that is W equal to FB that is the statement of archus principle okay now weight of the floating body is equal to the okay weight of the floating body is equal to the weight of the liquid displaced by its immersed part that is B and force okay weight of the body floating body that is equals to B force of the liquid this is the statement what does it mean second case you see here the body is you know initially it is a throat on the surface of water what happened it is a floating okay not completely okay not completely syn to the bottom it is a floating some kind of okay and this weight of the body will be equal to the displacement I mean displaced water or liquid by this body okay so this uh you know weight of the body as well as displac liquid all these you are going to learn in a class 11th fluids concept okay just you have to know what happens F uh FB and W relation got it so that's all you have to learn if W is greater than FB the body sinks if W is less than bind force of the liquid then it is floats if W is equals to FB then it is also float but it is a submerged just inside the surface of water so that W equals fbk we call it as a you know statement of of argumen is principle got it okay now let's move on to the applications of a flotation okay application of flotation so here we have few applications of a flotation the first one flotation of an iron ship next one flotation of a man what is the reason for that okay if the flotation of iron ship if you consider enter weight of the you know a ship is less than the bant force of the liquid that means bind force is are more in this case Okay in all these case weight of the body average average weight of the body okay average weight of the body is less than bind force of the liquid therefore it is a floating floating okay in all the cases flotation of a man flotation of ice water and a submarine and Iceberg next waves and balloons okay so all these are application of a flotation okay and you can write any applications of this uh you know flotation and after the lecture what do you have to do so first revise the today's lecture highlight important concept or questions then note down okay your doubt if any okay in your notebook so that we can ask in a next class okay so that's all for today's session then we'll meet you in the next session with a new chapter till then take care bye-bye