ICSE Class 9 Physics: Measurements and Experimentations - Chapter 1

hello everyone hope you all are doing good I am anjana from learnohub the free learning platform where you can study math science and SST absolutely free at learnohack.com [Music] in today&#39;s class we are going to discuss icse class 9 physics chapter 1 measurements and experimentations we have discussed the topic of different fundamental quantities and their SI units in the previous session also we have solved questions from exercise 1A so here we&#39;ll be discussing the topic measurement of length and solving questions from exercise 1B are you ready for the session measurement of length in our previous class we have begin the class with the measurement of the length and breadth of this board okay you remember I use this pen and a pencil to measure the length and breadth of this board later we have said that these are not standard measurements yes then we said we can use a meter scale in order to measure the length and breadth yes also we had a box whose length width and the height we are measuring using pen and pencil later we said we can use a meter scale or a measuring tab in order to measure this you will be getting correct and accurate value from wherever the measurement is done yes we know measurement of length that is length is measured in kilometers length is measured in meters length is measured in centimeters length is measured in millimeters and there are smaller other units to measure length now my question is here I have two things which are used in order to measure the length Okay we have a meter scale and here we have a measuring term okay normally we know that a meter scale is of length 1 meter which means it is 100 centimeters okay in this hundred centimeter now here we have a 30 centimeter scale okay 30 centimeter scale which you will be using in your math classes so here in this 30 centimeter scale you have one two three four up to 30. okay other than this you can see some smaller lines okay here if it is one this line will show 0.1 centimeter okay the first point that is here you will be having 0.1 centimeter so when you take if this is the starting that is 0 and here if you have the one that is this one okay between them you can find 10 lines okay the Fifth Line will be bigger one two three four five six seven eight nine ten here we will be having one so this is 0.5 centimeter and this is 0.1 centimeter 0.2 centimeter 0.3.4.5.6.7.8.9 and this is one now if you have a pencil okay you have to measure the length of the pencil if this pencil is kept here that is one end of the pencil you will be keeping at the zero here you will be keeping okay let&#39;s see up to here you have the length then you can easily say that the pencil is of length 10 centimeter now my question is if you are measuring something such that the value is somewhere here that is the other end of the object is here okay you can see that this is 0.5 then this will be 0.6 centimeter okay and this will be 0.7 centimeter okay but you can see the end of the object is here that is neither at 0.6 centimeter nor at 0.7 centimeter we can understand it lies between 0.6 centimeter and 0.7 centimeter in this case how do we make the measurement can we use this meter scale in order to measure can you use this measuring tap even in measuring tab the least value that you will be getting is 0.1 centimeter okay in this case we will understand there should be some other device that will help us measure the values is so we will be starting in this chapter about these devices that are used to measure smaller lengths okay for example I have this book I need to measure the thickness of the cardboard that is being used to make the book okay in this case do you think the meter of scale is going to help me no right can see that this thickness will be below 0.1 centimeter when it is below 0.1 centimeter you cannot use the meter scale to measure yes so we&#39;ll see what device can be used in order to measure the thickness of the cardboard of first you need to understand the least count of a measuring instrument what is least con it is very simple we have set about the meter scale about the scale ruler we have said okay in the ruler the smallest length that can be measured as 0.1 centimeter or one millimeter one millimeter is the smallest length that can be measured the smallest length that can be measured using the device is called the least count okay in case of a scale it is 0.1 centimeter okay now consider the stopwatch here you can see 65 10 15 20 25 30. okay between the 60 and 5 you can find other lines one two three four five six seven eight nine ten there are ten lines okay which means each one will be point five seconds this is 5 Seconds this is 10 seconds this is 15 seconds then each line will be 0.5 seconds so here from 0 to 1 we are getting a range right the range is equal to range is equal to we are taking this one centimeter minus zero okay that is one centimeter is arranged in this one centimeter how many divisions are there how many lines are there that we are counting okay this one centimeter is divided into 10 parts yes so dividing by that 10 you will be getting the least count value least count you are getting one centimeter by 10 which is equal to 0.1 centimeter same here this is 5 Seconds 5 seconds divided by 10 divisions so 5 divided by 10 you will be getting 0.5 seconds okay now what about this emitter what is emitter emitter is a device that is used to measure the current okay to measure current you will be using a meter smaller current can be measured using milliampeter micrometer etcetera whatever it is so here you can see 0 1 2 3 4 5. okay so if your reading is somewhere here okay your needle is somewhere here it is not 0 it is not one but you will be able to measure this is number of Divisions you can count one two three four five six seven eight nine ten so the range is 1 ampere minus 0 ampere number of divisions is 10 divisions which means each one of this line each one of this division will be showing you 0.1 ampere okay each one will be 0.1 ampere if my reading is here if my reader is here you can count this one two three four five okay it is at the fifth division H1 is 0.1 so 0.1 0.20.30.40.5 so 0.5 ampere is my current okay what if it is at this point okay what if my needle is here in this case it has crossed 2 okay then 2.1 2.2 2.3 2.4 2.5 2.62.7 it is a 2.7 so 2.7 amperes okay now these can be measured if the current is still smaller smaller currents we are measuring that is you cannot use an ammeter normal ammeter cannot be used to measure currents that is less than 0.1 ampere then you will be using Milli ampere and micro ammeters yes millimeters and micro ammeters will help us measure the current okay now if you take 0.1 centimeter the value 0.1 centimeter another value 0 point 1 2 centimeter then you have 0.123 centimeter you have 0.1234 centimeter so you are using different device and measuring the length of something okay when you measure the length with the first device you got 0.1 centimeter the second device you got 0.12 centimeter third device gave you 0.123 centimeter and the fourth device give you 0.1234 centimeter which one is more accurate okay which is a perfect value we can take it will be 0.1234 centimeters yes it is not 0.1 centimeter is not 0.12 centimeter or 0.123 centimeter this will be the most accurate value because the number of decimals are increasing yes the number of decimals are increasing so this one will be the same but the divisions that is the number of decimal points are increasing and that will make it more accurate so this is what the concept of least count is for every device the smallest value that can be measured is the least count clear so if you are using a millimeter okay if you&#39;re using the if you are taking the case of a milliampet in case of millimeter it will be like 0 1 2 3 4 5 so milliampere the current is measured in milliampere in that case what will be one division so here this is one Milli ampere this is 2 Milli ampere okay what is the range one Milli ampere minus zero okay you will be having 10 divisions 2 3 4 5 6 7 8 9 10. okay you will be having 10 division what does one division mean okay if your needle is at this point first point what does it mean what will be it be equal to here we have one millimeter so the least value that can be measured will be 0.1 milliampere 0.1 Milli ampere is the least value that can be measured using a millimeter we have discussed about meter scale using a meter scale you can only measure the least value that can be measured or the least count of a meter scale is 0.1 centimeter water we have to measure the length which is smaller than that in that case the devices that we are used or the instruments that can be used are first one is Vernier calipers and the second one is screw gauge okay so we&#39;ll be discussing in this class in detail about these two devices Vernier calipers and screw gauge which will be giving more accurate result principle of Vernier this is how a Vernier looks like so here there are two scales one is the main scale and second is the Vernier scale that is the scale the scale which is below you can call it the main scale on this main scale you will be having reading so here you can see up to 10 centimeter reading is there starting from 0 from 0 up to 10 centimeter reading is there okay so when you take the readings here you will be having 0 this is 1 this is 2 this is 3 up to 10 you will be having okay so when you take from 0 to 1 so what is it this is one centimeter right so up to point one each value will be 0.1 okay the very next value this is point one this is 0.2.3.4.5 this is a main scale reading now you can see another skill about this scale is a movable scale or a sliding scale this can be moved okay and the movement of the scale will help us give more accurate results so in this case we have said that in case of a meter scale you can measure values that is the least counter 0.1 centimeter so here when you use a Vernier the second decimal will be able to obtain the second decimal as well so the 0.1 centimeter is one millimeter okay using Vernier scale you will be able to get 0.1 millimeter or you can get 0.0 1 centimeter this will be the least count for example if you are getting the answer to be 1.28 centimeter you&#39;re measuring something and you&#39;re getting 1.28 centimeters so you can say that this measurement cannot be made using a meter skid you can use a Vernier scale because the second division that is the second decimal is also given so using the Vernier scale is how you will be able to find the length clear so this was a more accurate value compared to the previous one okay so these are the two scales and the second scale is helping you find the second decimal done clear so we&#39;ll be discussing in detail about the least count of a Vernier or we have to first find this is also called Vernier constant so first when you&#39;re using a Vernier calipers or a screw gauge you need to find the least conference so how to find the least con we said least count is the smallest value that can be measured now here in the main scale we have discussed what a main scale and what are Vernier scales so in the main scale let&#39;s take one centimeter okay 0 to 1 centimeter there will be 10 divisions here you will be having 0.5 so this is point one point two point three point four point five point six point seven point eight point nine one centimeter okay so this is 0.9 centimeter okay then you will be having a Vernier scale like in main scale main scale there are 10 divisions in Vernier scale or also there are 10 divisions but the thing is the 10th division on Vernier scale will be at this point nine centimeter okay so here the 0 will be here for the one year scale also 0 will be here okay 5 6 7 8 9 10. okay this is how the divisions would be that clear now you can see that this is 10 divisions okay so what is the value of one main scale division here it is one centimeter you can see that value of one main scale division this is the first main scale division while your one main scale division will be 0.1 centimeter total one centimeter divided by 10 so 0.1 centimeter now what about the Vernier scale division here you can see this is total 0.9 centimeter okay this 0.9 centimeter length is divided into 10 parts okay which means each part that is value of one Vernier scale reading or value of one when you scale reading how much do we get total we have 0.9 centimeter divided by 10 that is 0.09 centimeter so here it is given that the release count of a Vernier that is equal to the difference between the value of one main scale Division and one Vernier scale division that is least count will be equal to value of one main scale division you are getting 0.1 centimeter minus value of one Vernier scale division that is 0.09 centimeter what does this equal to you will be getting 0.01 centimeter that is the second decimal we are getting and the 0.01 centimeter is your least count of the Vernier okay now main scale divisions okay we can see that nine main scale division is equal to 10 Vernier scale divisions yes here we have 9 9th point this is okay ninth mark this is and this is equal to 10 divisions on the Vernier okay then you will be having Vernier scale division is equal to 9 by 10 into main scale division okay that is if you are taking the Vernier scale divisions that is we have 10 okay if you are taking this 10 as n n into Vernier scale division will be equal to what is 9 9 is n minus 1 okay n minus 1 main scale division or the Vernier scale division is equal to n minus 1 divided by n main scale division we have least count of Vernier or the Vernier constant equal to value of one main scale division minus value of one Vernier scale division then the least count you can write is equal to value of 1 Main scale division we will represent it as MSD main scale division minus value of 1 Vernier scale division is vsd n minus 1 divided by n into main scale division okay so main scale division is common MSD taken out then you will be having 1 minus n minus 1 divided by n okay this n can be taken here we are taking the LCM you will be getting MSD into n minus n plus 1 divided by n n minus n can be canceled then you will be having 1 by n what is it MSD divided by n what is n n is the number of Divisions on the Vernier scale okay therefore we can find least count value of one main scale division which is taken as x divided by total number of Divisions on the Vernier which is represented by n okay this is how you can find the least count of a Vernier or the Vernier con example one figure shows a main scale graduated to read up to one millimeter and Vernier scale on which the length of 10 division is equal to the length of 9 divisions on the main scale calculate the least count how to find least count first we need value of one main scale division value of 1 main scale division which is represented by X is equal to here what is it is given that one millimeter okay it is one millimeter what is the number of Divisions on Vernier scale number of divisions on Vernier scale is equal to given 10 divisions 10 divisions then the least count can be found least count will be equal to x divided by and value of one main scale division divided by total number of Divisions on the Vernier scale which is one millimeter divided by 10 that is 0.1 millimeter 0.1 millimeters is the least count of this instrument now how to measure with a Vernier scale this is how a Vernier skill looks like this is your main scale okay and you have this which is able to slide over the main scale so here you can see we are going to measure the length of a root this is 0 this is one one centimeter two centimeter etcetera okay now you can see that this is the total length of the root how to find the length of the root you can find this is 1.1 and this is 1.2 and the value that is the end lies between 1.2 and 1.3 it is up to here right up to here which means it has crossed 1.2 and is above 1.3 so you cannot take 1.2 or 1.3 okay the reading that can be measured on the main scale is 1.2 centimeter what about the remaining so to measure the remaining you will be using the Vernier scale that is when the devices that is the object that is to be measured the length should be measured is placed in between and there will be a screw which can be tightened you will be getting the values there okay so you can first note the main scale reading here the main scale reading is 1.2 centimeter now we need main scale reading is equal to 1.2 centimeter now we need the Vernier scale reading how to find the Vernier scale ready to find the Vernier scale in here you can see that this a b length Okay the main scale Reading Plus this a b length will give you the correct length of the root this a b length is a Vernier scale reading Vernier scale reading will be equal to to get Vernier skill reading first you have to find the least count here what is the least count this is one centimeter and there are 10 divisions therefore least count will be equal to main scale division value of one main scale division that is here it is 0.1 centimeter okay this is 0.1 centimeter number of Divisions on the Vernier scale here this is your Vernier scale number of division is equal to 10 divisions okay by 10 that is 0.01 centimeters after getting discount what you have to do is you have to find where the zero lies okay here we have the zero okay from this you have found the main scale division next thing you have to do is you should find the line that is coinciding with the line on Main scale okay take this is it coinciding no right so the next one when you check this it is also not coinciding this is not coinciding but when you take this these are coinciding yes these are coinciding so we have to take the value what is the value this is one two three four this coinciding value we take it as p p is equal to here it is 4. okay to get the Vernier scale reading you have to multiply p and the least count here 4 into 0.01 that is 0.04 okay therefore you will be having the length of Road is equal to main scale reading plus one year skill reading that is 1.2 centimeter plus 0.04 centimeter which is 1.24 centimeter so this is the most accurate length Okay if you&#39;re using a meter scale in that case you will be able to see it is 1.2 centimeter you won&#39;t get the accurate length of the root understood so here when you start before placing this road the zero of the main scale and the zero of the Vernier scale will be coincide okay when you place the object what happens the zero of the Vernier scale will be ahead of the zero of main scale here now let us understand the main parts of a Vernier caliper this is our Vernier caliper look like in a one year character you will be having the main scale why is main scale used to get the readings like point one centimeter 0.2 centimeter these readings you can get from the main scale when you have the Vernier scale we we have said that Warrior scale can be moving above the main scale okay you will be getting more accurate result using the Vernier scale that is 0.01 centimeter 0.02 centimeters that is up to Second decimal we will be getting the values when the Vernier scale is used okay and you can see the Vernier scale sliding over this overnia calipers are also called slide calipers now you can see that there are two joules that is first is the outside juice and the second is inside juice so outside juice this thing okay and the object will be placed here so here I can place this object and tighten it okay you will be having a screw the screw will be used to tighten after placing the object so the object will be placed between the Jaws J1 and J2 when you need to measure some length you need to measure the diameter of a sphere so in all these cases object will be placed here now why do we need this inside juice inside juice will be used when you need to measure some internal diameter or you need to measure the length or you need to measure the diameter of a hollow cylinder or if you have a pipe okay so this is a pipe pipe will be in the form of a hollow cylinder okay you cannot place it here why because in this case when you place you will be getting only the external diameter so that case you will be placing it here so between the inside Zoom you can find the internal diameter okay so for hollow objects to find internal diameter we will be using the inside juice so these two are the important parts and here we have the fixed end okay this is a fixed dough which won&#39;t be moving both these are fixed Jaws they won&#39;t be moving when an object is placed it is a Vernier scale that is moving and then these two joules here this and this will be moving yes okay now the third one it is a strip strip is this part okay here we have the strip so this strip is used in order to measure some depth okay if you need to measure the depth of a beaker depth of a beaker or of a bottle in that case you will be using the strip then you have the main scale and Vernier scale we know what the function of main scale and Vernier scale is yes to measure these values to get more accurate results at a 0.1 millimeter or 0.01 centimeter you will be using Vernier Square to measure help to measure correct up to zero point one centimeter or one millimeter we will be using the main scale we have studied the least count of over near least count of the Vernier can be determined using the x value and N value X is the value of one main scale Division and end is the total number of Divisions on the Vernier scale so here in order to get the least count that is if you want to decrease least count okay how to decrease please count to decrease lease count one thing that I can do is I can decrease the x value when x value decreases the least count will also decrease because they are directly proportional yes the number of Divisions we are holding constant and when I am decreasing the x value that is value of one main scale Division I can get the decreased lease count or the thing that can be done is this is kept constant and N value is increased since they are inversely proportional when the total number of Divisions on Vernier scale is increased least count will decrease so least count decreases when X decreases or n increases value of one main scale division decreases or the total number of Divisions on the Vernier scale increases okay zero error in Vernier calipers so when you bring the jaw J2 and J1 or Vernier calipers in touch if the zeros of the main scale and the zero of the Vernier scale is coinciding we say the one year calipers is free of zero errors if that is not the case if in that case when the zeros coincide the ninth division on the main scale and the tenth division on the Vernier scale will also be coincide if that is not the case we say there is a zero error that is the zero of main scale and the zero of Vernier scale will not be coinciding so the distance between the zero of main scale and the zero of Vernier scale is called the zero error there are two types of zero errors one is positive zero error and the second is negative zero error we&#39;ll discuss mnd first is positive zero error that is when J 1 and J A2 meats you can see that the zero of Vernier scale is above or in front of or to the right of the zero of main scale yes so here you can see the zeros are not coinciding that is the tenth division of the Vernier scale is not coinciding with the ninth division of the main scale here the error we call the positive zero error now how to find the positive zero error to calculate positive zero error we have to find the coinciding value so you can see that the sixth division okay so sixth division of the Vernier scale is coinciding with the main scale can see a straight line here okay so this is a coinciding division you take this value okay to find zero error when it is positive zero error we will be putting a positive sign you take this value that is 6 and then multiply it with the least count so here the main scale you can see one centimeter the smallest value it can be measured on the main scale is 0.1 centimeter 1 divided by 10 divisions so 0.01 centimeter is the least count which is equal to plus 0.06 centimeter in this case the positive zero error is plus 0.06 centimeter now to find the negative zero error in case of negative zero error you can see the zero Vernier scale will be to the left of the zero of main scale okay then the negative 0 error will be equal to since it is negative put the negative sign now what you have to do is you will have to subtract so here you have total 10 divisions from the stand division you will have to subtract the value so here what is the value coinciding value you can see 7 is the coin setting division okay 10 minus 7 into the least count which is 0.01 centimeters that is equal to minus 10 minus 7 is 3 3 into 0.01 which is 0.03 centimeters so the negative zero error in this case is 0.03 centimeter understood how to find the positive and negative zero error correction due to zero error how to get the correct or the perfect reading if you are getting the observed reading let&#39;s say it is equal to 2 point 4 6 centimeter okay The observed reading is 2.46 centimeter there is a zero error okay first let us take there is a positive zero here in case of positive 0 error the zero error is equal to positive let&#39;s say it is 0.02 centimeter this is the positive error in that case what you will be doing is you will be subtracting this value the zero error value with the sign you have to subtract remember that okay from The observed reading you will be subtracting the zero error to get the correct reading so here it will be 2.46 minus 0.02 that is 2.44 centimeter okay this will be the correct reading now in other case we&#39;ll say the same is the observed really for the device the zero error in this case it is minus 0.02 centimeter okay then minus of minus 0.02 centimeter here we are having negative zero error that is 2.46 plus 0.02 2.48 centimeter this will be your correct reading clear so when it is a positive zero error should remember there is a positive sign and you will be subtracting this value from The observed reading when it is a negative zero error here we have a negative sign and also this minus sign it becomes positive and the value we will be adding to the observed reading you will be getting the corrected measurement of length with Vernier caliper so here what we are going to do is we are going to measure the breadth of this AC remote using Vernier calipers before that first we need to collect some data regarding this Vernier calipers first the total number of Divisions on Vernier scale we need to find what is the total number of Divisions here we have 10 divisions okay value of one main scale division the smallest value that can be measured using the main scale it is 0.1 centimeter lease counters main scale division that is the value of one main scale division divided by total number of Divisions on the Vernier scale 0.1 divided by 10 you will be getting 0.01 centimeter and then you have to find the zero error so here if the zero of main scale and the zero of Vernier scale is not coinciding you will be getting zero error so when you take this when the Jews meet each other I can see that the zeros are not coinciding it is in front Okay Vernier skill zero is in front the value that is that is coinciding is one into the least count 0.01 so you will be getting 0.01 centimeter as a zero error since it is in front there will be a positive sign we are going to do this Experiment three times so for the first time place a remote here foreign so we have to take the main scale reading here the main scale reading is 39 and we need to find the Vernier division coinciding which is p okay here I am getting it to be 4. so 39 it is in the scaled which is in millimeters it is 39 millimeters which is 3.9 centimeters so this is 3.9 centimeters and the Vernier division that I am getting is 4. coinciding how will it coincide if this is the main scale division this is a one year scale division you can see they are in a straight line so this value on the Vernier scale will be taken so Vernier scale reading B will be equal to P into LC that is 4 into 0.01 which is the least count 0.04 Now The observed length is a plus b 3.9 plus 0.04 which is equal to 3.94 okay now the second time I&#39;m repeating it so placing it I&#39;m getting a value 39 as a main scale reading but now the coinciding value I can find is 5 okay on Vernier scale the 5 is coinciding with the main scale so 3.9 and 5 which is 5 into 0.01 equal to 0 point 0 5 3.9 plus 0.05 equal to 3.95 okay now the third time again once more you are going to do this so placing it I&#39;m getting 39 again as a main scale and now here we are getting 6 to be the coinciding value so 3.9 six six into zero point zero one which is equal to 0.06 therefore 3.9 plus 0.06 which is equal to 3.96 now we have to take the mean of all these observed lengths okay so mean reading will be equal to we have to add them 3.94 plus 3.95 plus 3.96 divided by 3. on adding what do we get you will be getting 11.85 divided by 3 which is equal to 3 point 9 5 okay 3.95 centimeters is the mean observed length okay so we have got the mean observed length to be equal to 3.95 centimeters to get the true value or the true length we know how to find the observed length observed like it will be main scale Reading Plus Vernier scale division that is p into the least count value so here we have got the observed length mean we have taken which is 3.95 we know what the zero error is zero error is plus 0.01 centimeter so true length will be equal to observe length that is 3.95 centimeter minus the zero error the sign is very important which is plus 0.01 centimeter that is equal to 3.95 centimeter minus 0.01 centimeter equal to 3.94 centimeters so this is the true length of the breadth of the correct value of the breadth of the AC remote that we have used now let us see how to read the Vernier Ed okay so here this is how it is this is your main scale and this is your vernous key now first we have to find the least count what will be the least count this case the least count will be for a normal Vernier calculate 0.01 centimeters okay here you can see this is your main scale this is one centimeter six minus 5 range you will be getting this is one centimeter one centimeter number of divisions is 10 1 centimeter by ten you will be getting 0 point one okay so the 0.1 is the value that can that we can read on using this main scale then we have to find the total number of Divisions on the Vernier scale that is equal to 10 divisions therefore 0.1 divided by 10 you will be getting 0.01 centimeter as a least count now what is the main scale Reading Main scale reading check the value so here it starts yes so this is 5 5.1 5.25.3 so the starting is 5.3 between 5.3 and 5.4 so you will be taking the solver value which is 5.3 centimeter now we have to find the P to find P you will have to check these values and you have to get a straight line that is about your scale reading that is coinciding with the main scale reading so you can find that this line okay this is a straight line counting this is 0 1 2 3 4 5 6 so 6 is the P value 6 is a p-value then what is the Vernier scale reading when you&#39;re scale reading is p into please count that is equal to 6 into 0.01 equal to 0.06 centimeters okay 0.06 centimeters now what is the observed reading observed reading will be equal to first the main scale reading here the main scale reading is 5.3 centimeter plus the Vernier reading when you&#39;re reading we got P into LC which is 0.06 centimeters 0.06 centimeters that is equal to 5.36 centimeters so if this Vernier calipers is free of zero error in that case the value that we read is 5.36 next we&#39;ll be discussing about screw gauge screw gauge is also a device that is used to measure length okay with accurate length can be measured so here first we need to understand the principle of a screw all now water screws this is how a screw looks like so you can tighten and loosen the screw that is when you rotate it in the clockwise and anti-clockwise directions it will be moving inside and outside we know this right that is forward and backward it will be moving now here you can see these These are called threads okay so when you make one complete rotation of the head so this is the head okay when you make a complete rotation of the head what happens is the screw will be moving this much distance forward okay so if you are rotating in the opposite direction it will be moving this this much distance backward that is between two consecutive threads the distance will be this much distance will be moved in a complete rotation of the head in one complete rotation this is a resistance move okay so in that case this is the case of a screw so in case of a screw gauge you will be having a head okay this is a circular head in the circular head there will be many divisions usually it will be 50 or it will be 100 divisions so when you rotate this okay there will be movement this will be moving forward and backward you can see the cylindrical part okay with this you can make the measurements clear okay so first we need to understand what is the pitch of a screw okay pitch of a screw is the distance moved by it in a complete rotation okay in one rotation how much distance it moves is called the pitch of the screen how to find the least count of a screw so if you know the pitch you know how to find the pitch pitches the distance mode by the screw in one complete rotation of the head okay let us say the pitch is equal to one millimeter that is window complete rotation is made the screw moves by distance of one millimeter and we have to find the total number of Divisions on the circular scale as we said on the circular scale or the circular head the total number of Divisions either it will be 50 or 100 if a case we are taking there are 100 divisions then the least count will be equal to the pitch of screw divided by total number of Divisions on the circular scale here one millimeter divided by 100 that is equal to zero point zero so one millimeter or 0.001 centimeter so this is how you can find the least common pitch and the total number of Divisions on the head scale is not you can find the least count here next example if a screw moves by one millimeter in one rotation and it has 50 divisions on its circular scale then find the pitch and least count of the screw so here first we have to find the pitch what is pitch pitches the distance moved by the screw in one rotation it is directly given which is one millimeter now least count is equal to pitch divided by number of Divisions on number of Divisions on circular head or the head scale which is equal to one millimeter divided by 50 divisions which is 0.02 millimeters so 0.02 millimeters is a please count in this case now this is the structure of a screw gauge let us discuss in detail about the parts of a screw gate so here you have a U-shaped frame okay then you have the cylindrical part this part is the circular scale or the head scale then you have a baseline this is your main scale this is the stud and here we have the screw this is spindle so when you place an object the object will be placed that is if you need to measure the thickness of something the object will be placed between the stud and the screw this is how you will be placing it and you will be rotating to tighten this okay now when you rotate what happens you can see this part will be moving so the main parts first is the circular scale we discussed this is a circular scale and this on the circular scale you will be having 50 or 100 divisions then you will be having the main scale to read length correct up to one millimeter or 0.1 centimeter we need the main scale main scale is this line or it is called the base light so when you are rotating you can see that this part will be touching any of these values and that reading will be take okay so the reading that is the value that comes in front you will be taking next you will be having the symbol to Mark the circular scale so here you will be having this thing okay so where it is moving that is a hollow cylindrical part next you have the Rashid to advance the screw by turning it till object is gently held between the stud and the spindle of screw so you can see that when the object is placed you need something to move that is a head should be rotated so that part here you have this okay so you will be rotating it what happens when you rotate you can tighten it that is object will be tight here so one thing you have to remember is whenever you are measuring something so if you need to measure the breadth of something okay in that case you will place object here and you will be rotating this okay on rotating you keep rotating and once you will be hearing a tuxo once you hear that you should not further rotate that value should be taken okay if it is to find the zero error or to find the correct exact value the reading main scale reading you will be getting only when you take the first when you first hear the sound you have to take that correct reading you should not tighten it move clear so pitch of a screw we have discussed now what is a pitch of a screw gauge this pitch of a skew gauge is a linear distance mode by its crew on the main scale when circular scale completes one full rotations so here we&#39;ll be having the zero Mark okay so when you take the zero Mark of this circular scale or the head scale from the zero Mark you will start and make a complete rotation and you will get a 0 again okay if it is 75 now this is 75 you make a complete rotation and here you end up with 75 which means one rotation is complete in this one rotation what happens this will be moving forward okay that is the screw will be moving forward on the Baseline you will be able to note the values so the distance that is mode will be the pitch of the screw gauge okay next the least count of a screw gauge we know to find the least count of a screw so release count of a screw gauge is the linear distance moved by its screw along the main scale when the circular scale is rotated by one division on it that is least count will be this distance moved in one rotation is called the pitch so pitch of the screw gauge divided by total number of division on its circular scale will give you the least count now how to decrease the least count we have studied how to decrease the least count of a Vernier caliper so least count of a screw gauge can be decreased by decreasing the pitch okay also least count of steel gauge can be decreased by increasing the number of divisions on head scale okay so there it was increasing the number of Divisions on Vernier scale so here it is increasing the number of Divisions on the head scale or the circular hit now what a zero error in a screw gauge we have studied the zero error in a one year calipers now how to find the zero error in a screw gauge here again you will be having positive 0 error and negative zero here we have understood what zero error is so when you take the device okay here we have the screw gauge so when you check the values that is this is your Baseline okay when the spindle and the stud touch each other that is when you rotate it and first the sound comes you will stop there okay when you stop you should find the value okay here you can see that this is your zero okay this is a zero on the head scale or the circular head and this is the zero of the Baseline you can see that this is below okay you can find a zero here and this 0 on the head scale is below this Baseline in that case we call it as positive zero error okay how to find positive zero error we have to take the value here it is 5 okay on the Baseline which line is coinciding here the value is 5 so 5 into find the least count let&#39;s say the least count of this screw gauge is equal to 0.001 centimeters therefore 5 into 0.001 centimeters which is equal to 0.005 centimeters so if this 0 is below the Baseline we call it as positive zero error and you will have the positive sign here now what about negative zero error in case of negative zero error how does the figure look like in that figure what will be there you will be having the 0 above the Baseline okay above the Baseline you will be having the zero in that case let&#39;s say it is 95 okay 95 is on the Baseline so how to find the negative 0 error negative zero error will be equal to 100 minus the value that is 95 into the least count at 0.001 centimeter here you have to remember when you take the negative 0 error when you take the negative 0 error you should put a negative sign which is equal to minus 5 into 0.001 centimeter equal to minus 0.005 centimeter this is the negative zero error understood to how to find the positive zero error and negative zero error if it is below zero is below the Baseline it is positive and above the Baseline if you have 0 then it is negative okay how to do measurement with a screw gauge here I am going to measure the thickness of this card using a screw gauge first we have to collect some details about the screw gauge to find the pitch of first of the screw how to find the pitch of the screw in one rotation what is the distance move here the distance moved in one rotation is 0.1 centimeter total number of Divisions on the circular scale there are hundred divisions then what is the least count of screw gauge leaves count is pitch divided by total number of Divisions 0.1 by 100 which is 0.001 centimeter next to fine zero error you have to tighten the screw gauge till you get the touch out once you hear you will stop okay you can find the zero error so here the 0 is above the Baseline okay 0 is above the Baseline so negative 0 error you will be having and the value is 99 therefore 100 minus 99 into the least count 0.001 which is equal to 100 minus 99 you will be getting it to be 1 okay therefore 0.001 centimeter is a zero error you have a negative sign negative zero error now we&#39;ll repeat this Experiment three times one two three so first time loosen the screw place a card here between the stud and the spindle tighten it so once you hear the sound will stop note the value here the main scale reading is 0.5 centimeters then we have to find the circular scale reading number of divisions of circular scale in line with the Baseline so here I am getting on the Baseline 30 okay therefore 30 into least count 0.001 centimeter which is equal to zero point zero three centimeters okay 0.03 centimeters Now The observed thickness is a plus b 0.5 plus 0.03 which is equal to zero point five three okay now again I&#39;m repeating it loosening the screw and placing it here tightening once I hear the thug sound I&#39;ll be stopping again I&#39;m getting the main scale 0.5 and now the Vernier scale is 31. 31 into 0.001 which is equal to 0.031 centimeters on adding 0.5 plus 0.0 3 1 which is equal to 0.531 okay now the third time again I&#39;m repeating it tightening the screw I&#39;m getting 0.5 and this value now I am getting it to be 29 so 29 into 0.001 which is equal to 0.029 centimeters so a plus b is 0.5 plus 0.029 equal to zero point 529 okay you&#39;re getting three decimal values now you have to find the mean mean of The observed thickness so we&#39;ll be adding this all these divided by three that is equal to 0.530 you will be getting the mean observed reading to be equal to 0.530 now to find the true thickness we have got the mean of The observed thickness which is equal to we got it to be equal to 0.530 centimeters we have calculated the zero error the zero error is negative zero error and the value is 0.001 centimeters now to get the true thickness you have to subtract the zero error from The observed thickness which is equal to 0.530 centimeter minus 0.001 centimeter which is equal to 0.529 centimeter so this is the true thickness the actual thickness of the car that we have used next one kind of error is Backlash error this is mainly due to the wear and tear of the threads so here when you keep rotating it in some cases what happened is the end of the screw it won&#39;t be moving okay that is it won&#39;t be so that is in one rotation it won&#39;t be moving in that case you will be having these kinds of error 2 in order to prevent this kinds of error what can be done is always make rotations in one directions so the next thing that you have to do is if you are if you need to change the direction of rotation in that case you will have to complete the rotation till it comes to a stop only then do the rotation further in the opposite direction okay so in this case you can prevent and in this way you can prevent the backlash error example three in an instrument there are 25 divisions on the Vernier scale which have length of 24 divisions of the main scale one centimeter on Main scale is divided in 20 equal parts find the least count what is the value of one main scale division here value of 1 main scale division is equal to is given that one centimeter on Main scale is divided in 20 equal parts which means it will be 1 by 20 centimeter okay now what is the total number of Divisions on the Vernier scale in an instrument there are 25 divisions on Vernier scale it is directly given number of divisions on the Vernier skin n is equal to 25 okay this is represented as x x is 1 by 20 centimeter a number of divisions is 25 how to find the least count of a Vernier least count is equal to value of 1 Main scale division divided by number of Divisions on the Vernier scale so that is X by n 1 by 20 divided by 25 which is equal to 1 by 20 into 25 equal to 1 by 500 so what is 1 by 500 you will be getting 0.002 centimeters in centimeters it is 0.002 centimeter so this is the least count of the given instrument clear next example for the lease count of a Vernier calipers is 0.01 centimeter and 0 error is plus 0.02 centimeter while measuring the length of a road the main scale reading is 4.8 centimeter and 6 division on the Vernier scale is in line with the marking on the main scale calculate the length of the room so here we have to calculate the length of root so length of root will be equal to observed reading minus zero error so here the zero error is given yes okay about is the least count given the least count is equal to 0.01 centimeter then zero error is given 0 error the sign is very important here it is positive Sign Plus 0.02 centimeter okay first we need to find the observed reading what is observe reading observed reading foreign Plus least count at we have to determine the value that is here it is given that sixth division on Vernier scale is in line with the marking on the main scale so that is the coinciding value on the Vernier scale we are taking which you represented by P okay so P into least count so here the P value is 6 and LC these count we have 0.01 putting the values MSR mean scale Reading Main scale reading is given that is 4.8 plus p is 6 into least count to 0.01 which is equal to 4.8 plus 0.06 that is 4 point 8 6. centimeter okay so the observed reading is 4.86 centimeter now from this observed reading we will be subtracting the zero error to get the length of the root so length of root is equal to observed reading which is 4.86 minus 0 error that is 0.02 here it is positive sign okay we will be getting 4.84 centimeter which is the actual length of the root clear example 5 the circular head of a screw gauge is divided into 50 divisions and the screw moves one millimeter head in two revolutions of the circular head find its pitch and least curve okay here what is given number of divisions [Music] on circular head is equal to 50. okay it is given the distance moved distance mode in two revolutions is equal to one millimeter what is one millimeter it is 0.1 centimeter okay then what is the distance moved in one revolution distance moved in one revolution will give you the pitch pitch is equal to so the a part we have to find the pitch pitch is equal to distance mood in one revolution that is 0.1 centimeter divided by 2 which is equal to 0.05 centimeter if you need it in millimeter 0.5 millimeters okay now next we have to find the least count we know least count is equal to in case of a screw gauge please count is equal to pitch divided by number of divisions on circular head which is equal to pitch we have determined zero point zero five centimeter divided by number of Divisions on circular head what is the number of Divisions which is 50. 50 it is given in the question is equal to 5 divided by 5000 or 1 by 1000 equal to 0.001 centimeters if it is in centimeters you will get this value or 0.01 millimeters okay so this is your fine lines now let us do numericals from exercise 1B exercise 1B question one a stopwatch has 10 divisions graduated between the 0 and 5 Second marks what is its least count we have to find the least count here we have to find the range first okay range is equal to 0 and 5 Seconds Mark which means 5 Seconds minus zero seconds will give you the range that is equal to 5 Seconds okay then what is the total number of Divisions number of divisions is given number of divisions is equal to 10 how to find the least count least count will be equal to range divided by number of divisions which is equal to 5 seconds divided by 10 that is 0.5 seconds therefore the least count of the given stopwatch is equal to 0.5 seconds question 4 of exercise 1B a boy uses Vernier calipers to measure the thickness of his pencil he measures it to be 1.4 millimeter if the zero error of Vernier calipers is plus 0.02 centimeter what is the correct thickness of pencil how to get the correct thickness correct thickness will be equal to observed reading minus 0 error what is given in the question observed reading is given observe reading is equal to 1.4 millimeter what is the zero error zero error is equal to plus 0.02 centimeter so first thing you the unit should be same here it is in millimeter and here it is in centimeter either you have to convert this into centimeter or you have to convert this into millimeters okay what is 0.02 centimeter in millimeters you will be getting plus 0.2 millimeters okay now we can find the correct thickness correct thickness is equal to 1.4 millimeters minus the zero error which is 0.2 millimeter is equal to 1.2 millimeter okay so 1.2 millimeter is the correct thickness of the pencil question 9 of exercise 1B the pitch of a screw gauge is 0.5 millimeter and the head scale is divided in 100 Parts what is the least count of a screw gauge very simple question right we know the pitch is given which is equal to 0.5 millimeters number of Divisions on head scale is given number of divisions on circular head is equal to 100 to divide into 100 parts means the number of division will be 100 then the least count is equal to pitch divided by number of divisions on circular head which is equal to 0.5 millimeter divided by 100 equal to 0.00 5 millimeter if you have to convert it into centimeters 0.0005 centimeters just remember this thing one centimeter is 10 millimeters okay then one millimeter will be 1 by 10 centimeter here 0.05 0.005 millimeters will be equal to 0.005 by 10 centimeter which is 0.0005 centimeters clear that&#39;s all for today in today&#39;s class we have discussed how to measure length using screw gauge and Vernier calipers we have studied the parts of these we have also solved problems related to this from exercise one we hope you all enjoyed the session I&#39;ll be back in the next session until then stay tuned to learn how free thank you

hello everyone hope you all are doing good I am anjana from learnohub the free learning platform where you can study math science and SST absolutely free at learnohack.com [Music] in today&amp;#39;s class we are going to discuss icse class 9 physics chapter 1 measurements and experimentations we have discussed the topic of different fundamental quantities and their SI units in the previous session also we have solved questions from exercise 1A so here we&amp;#39;ll be discussing the topic measurement of length and solving questions from exercise 1B are you ready for the session measurement of length in our previous class we have begin the class with the measurement of the length and breadth of this board okay you remember I use this pen and a pencil to measure the length and breadth of this board later we have said that these are not standard measurements yes then we said we can use a meter scale in order to measure the length and breadth yes also we had a box whose length width and the height we are measuring using pen and pencil later we said we can use a meter scale or a measuring tab in order to measure this you will be getting correct and accurate value from wherever the measurement is done yes we know measurement of length that is length is measured in kilometers length is measured in meters length is measured in centimeters length is measured in millimeters and there are smaller other units to measure length now my question is here I have two things which are used in order to measure the length Okay we have a meter scale and here we have a measuring term okay normally we know that a meter scale is of length 1 meter which means it is 100 centimeters okay in this hundred centimeter now here we have a 30 centimeter scale okay 30 centimeter scale which you will be using in your math classes so here in this 30 centimeter scale you have one two three four up to 30. okay other than this you can see some smaller lines okay here if it is one this line will show 0.1 centimeter okay the first point that is here you will be having 0.1 centimeter so when you take if this is the starting that is 0 and here if you have the one that is this one okay between them you can find 10 lines okay the Fifth Line will be bigger one two three four five six seven eight nine ten here we will be having one so this is 0.5 centimeter and this is 0.1 centimeter 0.2 centimeter 0.3.4.5.6.7.8.9 and this is one now if you have a pencil okay you have to measure the length of the pencil if this pencil is kept here that is one end of the pencil you will be keeping at the zero here you will be keeping okay let&amp;#39;s see up to here you have the length then you can easily say that the pencil is of length 10 centimeter now my question is if you are measuring something such that the value is somewhere here that is the other end of the object is here okay you can see that this is 0.5 then this will be 0.6 centimeter okay and this will be 0.7 centimeter okay but you can see the end of the object is here that is neither at 0.6 centimeter nor at 0.7 centimeter we can understand it lies between 0.6 centimeter and 0.7 centimeter in this case how do we make the measurement can we use this meter scale in order to measure can you use this measuring tap even in measuring tab the least value that you will be getting is 0.1 centimeter okay in this case we will understand there should be some other device that will help us measure the values is so we will be starting in this chapter about these devices that are used to measure smaller lengths okay for example I have this book I need to measure the thickness of the cardboard that is being used to make the book okay in this case do you think the meter of scale is going to help me no right can see that this thickness will be below 0.1 centimeter when it is below 0.1 centimeter you cannot use the meter scale to measure yes so we&amp;#39;ll see what device can be used in order to measure the thickness of the cardboard of first you need to understand the least count of a measuring instrument what is least con it is very simple we have set about the meter scale about the scale ruler we have said okay in the ruler the smallest length that can be measured as 0.1 centimeter or one millimeter one millimeter is the smallest length that can be measured the smallest length that can be measured using the device is called the least count okay in case of a scale it is 0.1 centimeter okay now consider the stopwatch here you can see 65 10 15 20 25 30. okay between the 60 and 5 you can find other lines one two three four five six seven eight nine ten there are ten lines okay which means each one will be point five seconds this is 5 Seconds this is 10 seconds this is 15 seconds then each line will be 0.5 seconds so here from 0 to 1 we are getting a range right the range is equal to range is equal to we are taking this one centimeter minus zero okay that is one centimeter is arranged in this one centimeter how many divisions are there how many lines are there that we are counting okay this one centimeter is divided into 10 parts yes so dividing by that 10 you will be getting the least count value least count you are getting one centimeter by 10 which is equal to 0.1 centimeter same here this is 5 Seconds 5 seconds divided by 10 divisions so 5 divided by 10 you will be getting 0.5 seconds okay now what about this emitter what is emitter emitter is a device that is used to measure the current okay to measure current you will be using a meter smaller current can be measured using milliampeter micrometer etcetera whatever it is so here you can see 0 1 2 3 4 5. okay so if your reading is somewhere here okay your needle is somewhere here it is not 0 it is not one but you will be able to measure this is number of Divisions you can count one two three four five six seven eight nine ten so the range is 1 ampere minus 0 ampere number of divisions is 10 divisions which means each one of this line each one of this division will be showing you 0.1 ampere okay each one will be 0.1 ampere if my reading is here if my reader is here you can count this one two three four five okay it is at the fifth division H1 is 0.1 so 0.1 0.20.30.40.5 so 0.5 ampere is my current okay what if it is at this point okay what if my needle is here in this case it has crossed 2 okay then 2.1 2.2 2.3 2.4 2.5 2.62.7 it is a 2.7 so 2.7 amperes okay now these can be measured if the current is still smaller smaller currents we are measuring that is you cannot use an ammeter normal ammeter cannot be used to measure currents that is less than 0.1 ampere then you will be using Milli ampere and micro ammeters yes millimeters and micro ammeters will help us measure the current okay now if you take 0.1 centimeter the value 0.1 centimeter another value 0 point 1 2 centimeter then you have 0.123 centimeter you have 0.1234 centimeter so you are using different device and measuring the length of something okay when you measure the length with the first device you got 0.1 centimeter the second device you got 0.12 centimeter third device gave you 0.123 centimeter and the fourth device give you 0.1234 centimeter which one is more accurate okay which is a perfect value we can take it will be 0.1234 centimeters yes it is not 0.1 centimeter is not 0.12 centimeter or 0.123 centimeter this will be the most accurate value because the number of decimals are increasing yes the number of decimals are increasing so this one will be the same but the divisions that is the number of decimal points are increasing and that will make it more accurate so this is what the concept of least count is for every device the smallest value that can be measured is the least count clear so if you are using a millimeter okay if you&amp;#39;re using the if you are taking the case of a milliampet in case of millimeter it will be like 0 1 2 3 4 5 so milliampere the current is measured in milliampere in that case what will be one division so here this is one Milli ampere this is 2 Milli ampere okay what is the range one Milli ampere minus zero okay you will be having 10 divisions 2 3 4 5 6 7 8 9 10. okay you will be having 10 division what does one division mean okay if your needle is at this point first point what does it mean what will be it be equal to here we have one millimeter so the least value that can be measured will be 0.1 milliampere 0.1 Milli ampere is the least value that can be measured using a millimeter we have discussed about meter scale using a meter scale you can only measure the least value that can be measured or the least count of a meter scale is 0.1 centimeter water we have to measure the length which is smaller than that in that case the devices that we are used or the instruments that can be used are first one is Vernier calipers and the second one is screw gauge okay so we&amp;#39;ll be discussing in this class in detail about these two devices Vernier calipers and screw gauge which will be giving more accurate result principle of Vernier this is how a Vernier looks like so here there are two scales one is the main scale and second is the Vernier scale that is the scale the scale which is below you can call it the main scale on this main scale you will be having reading so here you can see up to 10 centimeter reading is there starting from 0 from 0 up to 10 centimeter reading is there okay so when you take the readings here you will be having 0 this is 1 this is 2 this is 3 up to 10 you will be having okay so when you take from 0 to 1 so what is it this is one centimeter right so up to point one each value will be 0.1 okay the very next value this is point one this is 0.2.3.4.5 this is a main scale reading now you can see another skill about this scale is a movable scale or a sliding scale this can be moved okay and the movement of the scale will help us give more accurate results so in this case we have said that in case of a meter scale you can measure values that is the least counter 0.1 centimeter so here when you use a Vernier the second decimal will be able to obtain the second decimal as well so the 0.1 centimeter is one millimeter okay using Vernier scale you will be able to get 0.1 millimeter or you can get 0.0 1 centimeter this will be the least count for example if you are getting the answer to be 1.28 centimeter you&amp;#39;re measuring something and you&amp;#39;re getting 1.28 centimeters so you can say that this measurement cannot be made using a meter skid you can use a Vernier scale because the second division that is the second decimal is also given so using the Vernier scale is how you will be able to find the length clear so this was a more accurate value compared to the previous one okay so these are the two scales and the second scale is helping you find the second decimal done clear so we&amp;#39;ll be discussing in detail about the least count of a Vernier or we have to first find this is also called Vernier constant so first when you&amp;#39;re using a Vernier calipers or a screw gauge you need to find the least conference so how to find the least con we said least count is the smallest value that can be measured now here in the main scale we have discussed what a main scale and what are Vernier scales so in the main scale let&amp;#39;s take one centimeter okay 0 to 1 centimeter there will be 10 divisions here you will be having 0.5 so this is point one point two point three point four point five point six point seven point eight point nine one centimeter okay so this is 0.9 centimeter okay then you will be having a Vernier scale like in main scale main scale there are 10 divisions in Vernier scale or also there are 10 divisions but the thing is the 10th division on Vernier scale will be at this point nine centimeter okay so here the 0 will be here for the one year scale also 0 will be here okay 5 6 7 8 9 10. okay this is how the divisions would be that clear now you can see that this is 10 divisions okay so what is the value of one main scale division here it is one centimeter you can see that value of one main scale division this is the first main scale division while your one main scale division will be 0.1 centimeter total one centimeter divided by 10 so 0.1 centimeter now what about the Vernier scale division here you can see this is total 0.9 centimeter okay this 0.9 centimeter length is divided into 10 parts okay which means each part that is value of one Vernier scale reading or value of one when you scale reading how much do we get total we have 0.9 centimeter divided by 10 that is 0.09 centimeter so here it is given that the release count of a Vernier that is equal to the difference between the value of one main scale Division and one Vernier scale division that is least count will be equal to value of one main scale division you are getting 0.1 centimeter minus value of one Vernier scale division that is 0.09 centimeter what does this equal to you will be getting 0.01 centimeter that is the second decimal we are getting and the 0.01 centimeter is your least count of the Vernier okay now main scale divisions okay we can see that nine main scale division is equal to 10 Vernier scale divisions yes here we have 9 9th point this is okay ninth mark this is and this is equal to 10 divisions on the Vernier okay then you will be having Vernier scale division is equal to 9 by 10 into main scale division okay that is if you are taking the Vernier scale divisions that is we have 10 okay if you are taking this 10 as n n into Vernier scale division will be equal to what is 9 9 is n minus 1 okay n minus 1 main scale division or the Vernier scale division is equal to n minus 1 divided by n main scale division we have least count of Vernier or the Vernier constant equal to value of one main scale division minus value of one Vernier scale division then the least count you can write is equal to value of 1 Main scale division we will represent it as MSD main scale division minus value of 1 Vernier scale division is vsd n minus 1 divided by n into main scale division okay so main scale division is common MSD taken out then you will be having 1 minus n minus 1 divided by n okay this n can be taken here we are taking the LCM you will be getting MSD into n minus n plus 1 divided by n n minus n can be canceled then you will be having 1 by n what is it MSD divided by n what is n n is the number of Divisions on the Vernier scale okay therefore we can find least count value of one main scale division which is taken as x divided by total number of Divisions on the Vernier which is represented by n okay this is how you can find the least count of a Vernier or the Vernier con example one figure shows a main scale graduated to read up to one millimeter and Vernier scale on which the length of 10 division is equal to the length of 9 divisions on the main scale calculate the least count how to find least count first we need value of one main scale division value of 1 main scale division which is represented by X is equal to here what is it is given that one millimeter okay it is one millimeter what is the number of Divisions on Vernier scale number of divisions on Vernier scale is equal to given 10 divisions 10 divisions then the least count can be found least count will be equal to x divided by and value of one main scale division divided by total number of Divisions on the Vernier scale which is one millimeter divided by 10 that is 0.1 millimeter 0.1 millimeters is the least count of this instrument now how to measure with a Vernier scale this is how a Vernier skill looks like this is your main scale okay and you have this which is able to slide over the main scale so here you can see we are going to measure the length of a root this is 0 this is one one centimeter two centimeter etcetera okay now you can see that this is the total length of the root how to find the length of the root you can find this is 1.1 and this is 1.2 and the value that is the end lies between 1.2 and 1.3 it is up to here right up to here which means it has crossed 1.2 and is above 1.3 so you cannot take 1.2 or 1.3 okay the reading that can be measured on the main scale is 1.2 centimeter what about the remaining so to measure the remaining you will be using the Vernier scale that is when the devices that is the object that is to be measured the length should be measured is placed in between and there will be a screw which can be tightened you will be getting the values there okay so you can first note the main scale reading here the main scale reading is 1.2 centimeter now we need main scale reading is equal to 1.2 centimeter now we need the Vernier scale reading how to find the Vernier scale ready to find the Vernier scale in here you can see that this a b length Okay the main scale Reading Plus this a b length will give you the correct length of the root this a b length is a Vernier scale reading Vernier scale reading will be equal to to get Vernier skill reading first you have to find the least count here what is the least count this is one centimeter and there are 10 divisions therefore least count will be equal to main scale division value of one main scale division that is here it is 0.1 centimeter okay this is 0.1 centimeter number of Divisions on the Vernier scale here this is your Vernier scale number of division is equal to 10 divisions okay by 10 that is 0.01 centimeters after getting discount what you have to do is you have to find where the zero lies okay here we have the zero okay from this you have found the main scale division next thing you have to do is you should find the line that is coinciding with the line on Main scale okay take this is it coinciding no right so the next one when you check this it is also not coinciding this is not coinciding but when you take this these are coinciding yes these are coinciding so we have to take the value what is the value this is one two three four this coinciding value we take it as p p is equal to here it is 4. okay to get the Vernier scale reading you have to multiply p and the least count here 4 into 0.01 that is 0.04 okay therefore you will be having the length of Road is equal to main scale reading plus one year skill reading that is 1.2 centimeter plus 0.04 centimeter which is 1.24 centimeter so this is the most accurate length Okay if you&amp;#39;re using a meter scale in that case you will be able to see it is 1.2 centimeter you won&amp;#39;t get the accurate length of the root understood so here when you start before placing this road the zero of the main scale and the zero of the Vernier scale will be coincide okay when you place the object what happens the zero of the Vernier scale will be ahead of the zero of main scale here now let us understand the main parts of a Vernier caliper this is our Vernier caliper look like in a one year character you will be having the main scale why is main scale used to get the readings like point one centimeter 0.2 centimeter these readings you can get from the main scale when you have the Vernier scale we we have said that Warrior scale can be moving above the main scale okay you will be getting more accurate result using the Vernier scale that is 0.01 centimeter 0.02 centimeters that is up to Second decimal we will be getting the values when the Vernier scale is used okay and you can see the Vernier scale sliding over this overnia calipers are also called slide calipers now you can see that there are two joules that is first is the outside juice and the second is inside juice so outside juice this thing okay and the object will be placed here so here I can place this object and tighten it okay you will be having a screw the screw will be used to tighten after placing the object so the object will be placed between the Jaws J1 and J2 when you need to measure some length you need to measure the diameter of a sphere so in all these cases object will be placed here now why do we need this inside juice inside juice will be used when you need to measure some internal diameter or you need to measure the length or you need to measure the diameter of a hollow cylinder or if you have a pipe okay so this is a pipe pipe will be in the form of a hollow cylinder okay you cannot place it here why because in this case when you place you will be getting only the external diameter so that case you will be placing it here so between the inside Zoom you can find the internal diameter okay so for hollow objects to find internal diameter we will be using the inside juice so these two are the important parts and here we have the fixed end okay this is a fixed dough which won&amp;#39;t be moving both these are fixed Jaws they won&amp;#39;t be moving when an object is placed it is a Vernier scale that is moving and then these two joules here this and this will be moving yes okay now the third one it is a strip strip is this part okay here we have the strip so this strip is used in order to measure some depth okay if you need to measure the depth of a beaker depth of a beaker or of a bottle in that case you will be using the strip then you have the main scale and Vernier scale we know what the function of main scale and Vernier scale is yes to measure these values to get more accurate results at a 0.1 millimeter or 0.01 centimeter you will be using Vernier Square to measure help to measure correct up to zero point one centimeter or one millimeter we will be using the main scale we have studied the least count of over near least count of the Vernier can be determined using the x value and N value X is the value of one main scale Division and end is the total number of Divisions on the Vernier scale so here in order to get the least count that is if you want to decrease least count okay how to decrease please count to decrease lease count one thing that I can do is I can decrease the x value when x value decreases the least count will also decrease because they are directly proportional yes the number of Divisions we are holding constant and when I am decreasing the x value that is value of one main scale Division I can get the decreased lease count or the thing that can be done is this is kept constant and N value is increased since they are inversely proportional when the total number of Divisions on Vernier scale is increased least count will decrease so least count decreases when X decreases or n increases value of one main scale division decreases or the total number of Divisions on the Vernier scale increases okay zero error in Vernier calipers so when you bring the jaw J2 and J1 or Vernier calipers in touch if the zeros of the main scale and the zero of the Vernier scale is coinciding we say the one year calipers is free of zero errors if that is not the case if in that case when the zeros coincide the ninth division on the main scale and the tenth division on the Vernier scale will also be coincide if that is not the case we say there is a zero error that is the zero of main scale and the zero of Vernier scale will not be coinciding so the distance between the zero of main scale and the zero of Vernier scale is called the zero error there are two types of zero errors one is positive zero error and the second is negative zero error we&amp;#39;ll discuss mnd first is positive zero error that is when J 1 and J A2 meats you can see that the zero of Vernier scale is above or in front of or to the right of the zero of main scale yes so here you can see the zeros are not coinciding that is the tenth division of the Vernier scale is not coinciding with the ninth division of the main scale here the error we call the positive zero error now how to find the positive zero error to calculate positive zero error we have to find the coinciding value so you can see that the sixth division okay so sixth division of the Vernier scale is coinciding with the main scale can see a straight line here okay so this is a coinciding division you take this value okay to find zero error when it is positive zero error we will be putting a positive sign you take this value that is 6 and then multiply it with the least count so here the main scale you can see one centimeter the smallest value it can be measured on the main scale is 0.1 centimeter 1 divided by 10 divisions so 0.01 centimeter is the least count which is equal to plus 0.06 centimeter in this case the positive zero error is plus 0.06 centimeter now to find the negative zero error in case of negative zero error you can see the zero Vernier scale will be to the left of the zero of main scale okay then the negative 0 error will be equal to since it is negative put the negative sign now what you have to do is you will have to subtract so here you have total 10 divisions from the stand division you will have to subtract the value so here what is the value coinciding value you can see 7 is the coin setting division okay 10 minus 7 into the least count which is 0.01 centimeters that is equal to minus 10 minus 7 is 3 3 into 0.01 which is 0.03 centimeters so the negative zero error in this case is 0.03 centimeter understood how to find the positive and negative zero error correction due to zero error how to get the correct or the perfect reading if you are getting the observed reading let&amp;#39;s say it is equal to 2 point 4 6 centimeter okay The observed reading is 2.46 centimeter there is a zero error okay first let us take there is a positive zero here in case of positive 0 error the zero error is equal to positive let&amp;#39;s say it is 0.02 centimeter this is the positive error in that case what you will be doing is you will be subtracting this value the zero error value with the sign you have to subtract remember that okay from The observed reading you will be subtracting the zero error to get the correct reading so here it will be 2.46 minus 0.02 that is 2.44 centimeter okay this will be the correct reading now in other case we&amp;#39;ll say the same is the observed really for the device the zero error in this case it is minus 0.02 centimeter okay then minus of minus 0.02 centimeter here we are having negative zero error that is 2.46 plus 0.02 2.48 centimeter this will be your correct reading clear so when it is a positive zero error should remember there is a positive sign and you will be subtracting this value from The observed reading when it is a negative zero error here we have a negative sign and also this minus sign it becomes positive and the value we will be adding to the observed reading you will be getting the corrected measurement of length with Vernier caliper so here what we are going to do is we are going to measure the breadth of this AC remote using Vernier calipers before that first we need to collect some data regarding this Vernier calipers first the total number of Divisions on Vernier scale we need to find what is the total number of Divisions here we have 10 divisions okay value of one main scale division the smallest value that can be measured using the main scale it is 0.1 centimeter lease counters main scale division that is the value of one main scale division divided by total number of Divisions on the Vernier scale 0.1 divided by 10 you will be getting 0.01 centimeter and then you have to find the zero error so here if the zero of main scale and the zero of Vernier scale is not coinciding you will be getting zero error so when you take this when the Jews meet each other I can see that the zeros are not coinciding it is in front Okay Vernier skill zero is in front the value that is that is coinciding is one into the least count 0.01 so you will be getting 0.01 centimeter as a zero error since it is in front there will be a positive sign we are going to do this Experiment three times so for the first time place a remote here foreign so we have to take the main scale reading here the main scale reading is 39 and we need to find the Vernier division coinciding which is p okay here I am getting it to be 4. so 39 it is in the scaled which is in millimeters it is 39 millimeters which is 3.9 centimeters so this is 3.9 centimeters and the Vernier division that I am getting is 4. coinciding how will it coincide if this is the main scale division this is a one year scale division you can see they are in a straight line so this value on the Vernier scale will be taken so Vernier scale reading B will be equal to P into LC that is 4 into 0.01 which is the least count 0.04 Now The observed length is a plus b 3.9 plus 0.04 which is equal to 3.94 okay now the second time I&amp;#39;m repeating it so placing it I&amp;#39;m getting a value 39 as a main scale reading but now the coinciding value I can find is 5 okay on Vernier scale the 5 is coinciding with the main scale so 3.9 and 5 which is 5 into 0.01 equal to 0 point 0 5 3.9 plus 0.05 equal to 3.95 okay now the third time again once more you are going to do this so placing it I&amp;#39;m getting 39 again as a main scale and now here we are getting 6 to be the coinciding value so 3.9 six six into zero point zero one which is equal to 0.06 therefore 3.9 plus 0.06 which is equal to 3.96 now we have to take the mean of all these observed lengths okay so mean reading will be equal to we have to add them 3.94 plus 3.95 plus 3.96 divided by 3. on adding what do we get you will be getting 11.85 divided by 3 which is equal to 3 point 9 5 okay 3.95 centimeters is the mean observed length okay so we have got the mean observed length to be equal to 3.95 centimeters to get the true value or the true length we know how to find the observed length observed like it will be main scale Reading Plus Vernier scale division that is p into the least count value so here we have got the observed length mean we have taken which is 3.95 we know what the zero error is zero error is plus 0.01 centimeter so true length will be equal to observe length that is 3.95 centimeter minus the zero error the sign is very important which is plus 0.01 centimeter that is equal to 3.95 centimeter minus 0.01 centimeter equal to 3.94 centimeters so this is the true length of the breadth of the correct value of the breadth of the AC remote that we have used now let us see how to read the Vernier Ed okay so here this is how it is this is your main scale and this is your vernous key now first we have to find the least count what will be the least count this case the least count will be for a normal Vernier calculate 0.01 centimeters okay here you can see this is your main scale this is one centimeter six minus 5 range you will be getting this is one centimeter one centimeter number of divisions is 10 1 centimeter by ten you will be getting 0 point one okay so the 0.1 is the value that can that we can read on using this main scale then we have to find the total number of Divisions on the Vernier scale that is equal to 10 divisions therefore 0.1 divided by 10 you will be getting 0.01 centimeter as a least count now what is the main scale Reading Main scale reading check the value so here it starts yes so this is 5 5.1 5.25.3 so the starting is 5.3 between 5.3 and 5.4 so you will be taking the solver value which is 5.3 centimeter now we have to find the P to find P you will have to check these values and you have to get a straight line that is about your scale reading that is coinciding with the main scale reading so you can find that this line okay this is a straight line counting this is 0 1 2 3 4 5 6 so 6 is the P value 6 is a p-value then what is the Vernier scale reading when you&amp;#39;re scale reading is p into please count that is equal to 6 into 0.01 equal to 0.06 centimeters okay 0.06 centimeters now what is the observed reading observed reading will be equal to first the main scale reading here the main scale reading is 5.3 centimeter plus the Vernier reading when you&amp;#39;re reading we got P into LC which is 0.06 centimeters 0.06 centimeters that is equal to 5.36 centimeters so if this Vernier calipers is free of zero error in that case the value that we read is 5.36 next we&amp;#39;ll be discussing about screw gauge screw gauge is also a device that is used to measure length okay with accurate length can be measured so here first we need to understand the principle of a screw all now water screws this is how a screw looks like so you can tighten and loosen the screw that is when you rotate it in the clockwise and anti-clockwise directions it will be moving inside and outside we know this right that is forward and backward it will be moving now here you can see these These are called threads okay so when you make one complete rotation of the head so this is the head okay when you make a complete rotation of the head what happens is the screw will be moving this much distance forward okay so if you are rotating in the opposite direction it will be moving this this much distance backward that is between two consecutive threads the distance will be this much distance will be moved in a complete rotation of the head in one complete rotation this is a resistance move okay so in that case this is the case of a screw so in case of a screw gauge you will be having a head okay this is a circular head in the circular head there will be many divisions usually it will be 50 or it will be 100 divisions so when you rotate this okay there will be movement this will be moving forward and backward you can see the cylindrical part okay with this you can make the measurements clear okay so first we need to understand what is the pitch of a screw okay pitch of a screw is the distance moved by it in a complete rotation okay in one rotation how much distance it moves is called the pitch of the screen how to find the least count of a screw so if you know the pitch you know how to find the pitch pitches the distance mode by the screw in one complete rotation of the head okay let us say the pitch is equal to one millimeter that is window complete rotation is made the screw moves by distance of one millimeter and we have to find the total number of Divisions on the circular scale as we said on the circular scale or the circular head the total number of Divisions either it will be 50 or 100 if a case we are taking there are 100 divisions then the least count will be equal to the pitch of screw divided by total number of Divisions on the circular scale here one millimeter divided by 100 that is equal to zero point zero so one millimeter or 0.001 centimeter so this is how you can find the least common pitch and the total number of Divisions on the head scale is not you can find the least count here next example if a screw moves by one millimeter in one rotation and it has 50 divisions on its circular scale then find the pitch and least count of the screw so here first we have to find the pitch what is pitch pitches the distance moved by the screw in one rotation it is directly given which is one millimeter now least count is equal to pitch divided by number of Divisions on number of Divisions on circular head or the head scale which is equal to one millimeter divided by 50 divisions which is 0.02 millimeters so 0.02 millimeters is a please count in this case now this is the structure of a screw gauge let us discuss in detail about the parts of a screw gate so here you have a U-shaped frame okay then you have the cylindrical part this part is the circular scale or the head scale then you have a baseline this is your main scale this is the stud and here we have the screw this is spindle so when you place an object the object will be placed that is if you need to measure the thickness of something the object will be placed between the stud and the screw this is how you will be placing it and you will be rotating to tighten this okay now when you rotate what happens you can see this part will be moving so the main parts first is the circular scale we discussed this is a circular scale and this on the circular scale you will be having 50 or 100 divisions then you will be having the main scale to read length correct up to one millimeter or 0.1 centimeter we need the main scale main scale is this line or it is called the base light so when you are rotating you can see that this part will be touching any of these values and that reading will be take okay so the reading that is the value that comes in front you will be taking next you will be having the symbol to Mark the circular scale so here you will be having this thing okay so where it is moving that is a hollow cylindrical part next you have the Rashid to advance the screw by turning it till object is gently held between the stud and the spindle of screw so you can see that when the object is placed you need something to move that is a head should be rotated so that part here you have this okay so you will be rotating it what happens when you rotate you can tighten it that is object will be tight here so one thing you have to remember is whenever you are measuring something so if you need to measure the breadth of something okay in that case you will place object here and you will be rotating this okay on rotating you keep rotating and once you will be hearing a tuxo once you hear that you should not further rotate that value should be taken okay if it is to find the zero error or to find the correct exact value the reading main scale reading you will be getting only when you take the first when you first hear the sound you have to take that correct reading you should not tighten it move clear so pitch of a screw we have discussed now what is a pitch of a screw gauge this pitch of a skew gauge is a linear distance mode by its crew on the main scale when circular scale completes one full rotations so here we&amp;#39;ll be having the zero Mark okay so when you take the zero Mark of this circular scale or the head scale from the zero Mark you will start and make a complete rotation and you will get a 0 again okay if it is 75 now this is 75 you make a complete rotation and here you end up with 75 which means one rotation is complete in this one rotation what happens this will be moving forward okay that is the screw will be moving forward on the Baseline you will be able to note the values so the distance that is mode will be the pitch of the screw gauge okay next the least count of a screw gauge we know to find the least count of a screw so release count of a screw gauge is the linear distance moved by its screw along the main scale when the circular scale is rotated by one division on it that is least count will be this distance moved in one rotation is called the pitch so pitch of the screw gauge divided by total number of division on its circular scale will give you the least count now how to decrease the least count we have studied how to decrease the least count of a Vernier caliper so least count of a screw gauge can be decreased by decreasing the pitch okay also least count of steel gauge can be decreased by increasing the number of divisions on head scale okay so there it was increasing the number of Divisions on Vernier scale so here it is increasing the number of Divisions on the head scale or the circular hit now what a zero error in a screw gauge we have studied the zero error in a one year calipers now how to find the zero error in a screw gauge here again you will be having positive 0 error and negative zero here we have understood what zero error is so when you take the device okay here we have the screw gauge so when you check the values that is this is your Baseline okay when the spindle and the stud touch each other that is when you rotate it and first the sound comes you will stop there okay when you stop you should find the value okay here you can see that this is your zero okay this is a zero on the head scale or the circular head and this is the zero of the Baseline you can see that this is below okay you can find a zero here and this 0 on the head scale is below this Baseline in that case we call it as positive zero error okay how to find positive zero error we have to take the value here it is 5 okay on the Baseline which line is coinciding here the value is 5 so 5 into find the least count let&amp;#39;s say the least count of this screw gauge is equal to 0.001 centimeters therefore 5 into 0.001 centimeters which is equal to 0.005 centimeters so if this 0 is below the Baseline we call it as positive zero error and you will have the positive sign here now what about negative zero error in case of negative zero error how does the figure look like in that figure what will be there you will be having the 0 above the Baseline okay above the Baseline you will be having the zero in that case let&amp;#39;s say it is 95 okay 95 is on the Baseline so how to find the negative 0 error negative zero error will be equal to 100 minus the value that is 95 into the least count at 0.001 centimeter here you have to remember when you take the negative 0 error when you take the negative 0 error you should put a negative sign which is equal to minus 5 into 0.001 centimeter equal to minus 0.005 centimeter this is the negative zero error understood to how to find the positive zero error and negative zero error if it is below zero is below the Baseline it is positive and above the Baseline if you have 0 then it is negative okay how to do measurement with a screw gauge here I am going to measure the thickness of this card using a screw gauge first we have to collect some details about the screw gauge to find the pitch of first of the screw how to find the pitch of the screw in one rotation what is the distance move here the distance moved in one rotation is 0.1 centimeter total number of Divisions on the circular scale there are hundred divisions then what is the least count of screw gauge leaves count is pitch divided by total number of Divisions 0.1 by 100 which is 0.001 centimeter next to fine zero error you have to tighten the screw gauge till you get the touch out once you hear you will stop okay you can find the zero error so here the 0 is above the Baseline okay 0 is above the Baseline so negative 0 error you will be having and the value is 99 therefore 100 minus 99 into the least count 0.001 which is equal to 100 minus 99 you will be getting it to be 1 okay therefore 0.001 centimeter is a zero error you have a negative sign negative zero error now we&amp;#39;ll repeat this Experiment three times one two three so first time loosen the screw place a card here between the stud and the spindle tighten it so once you hear the sound will stop note the value here the main scale reading is 0.5 centimeters then we have to find the circular scale reading number of divisions of circular scale in line with the Baseline so here I am getting on the Baseline 30 okay therefore 30 into least count 0.001 centimeter which is equal to zero point zero three centimeters okay 0.03 centimeters Now The observed thickness is a plus b 0.5 plus 0.03 which is equal to zero point five three okay now again I&amp;#39;m repeating it loosening the screw and placing it here tightening once I hear the thug sound I&amp;#39;ll be stopping again I&amp;#39;m getting the main scale 0.5 and now the Vernier scale is 31. 31 into 0.001 which is equal to 0.031 centimeters on adding 0.5 plus 0.0 3 1 which is equal to 0.531 okay now the third time again I&amp;#39;m repeating it tightening the screw I&amp;#39;m getting 0.5 and this value now I am getting it to be 29 so 29 into 0.001 which is equal to 0.029 centimeters so a plus b is 0.5 plus 0.029 equal to zero point 529 okay you&amp;#39;re getting three decimal values now you have to find the mean mean of The observed thickness so we&amp;#39;ll be adding this all these divided by three that is equal to 0.530 you will be getting the mean observed reading to be equal to 0.530 now to find the true thickness we have got the mean of The observed thickness which is equal to we got it to be equal to 0.530 centimeters we have calculated the zero error the zero error is negative zero error and the value is 0.001 centimeters now to get the true thickness you have to subtract the zero error from The observed thickness which is equal to 0.530 centimeter minus 0.001 centimeter which is equal to 0.529 centimeter so this is the true thickness the actual thickness of the car that we have used next one kind of error is Backlash error this is mainly due to the wear and tear of the threads so here when you keep rotating it in some cases what happened is the end of the screw it won&amp;#39;t be moving okay that is it won&amp;#39;t be so that is in one rotation it won&amp;#39;t be moving in that case you will be having these kinds of error 2 in order to prevent this kinds of error what can be done is always make rotations in one directions so the next thing that you have to do is if you are if you need to change the direction of rotation in that case you will have to complete the rotation till it comes to a stop only then do the rotation further in the opposite direction okay so in this case you can prevent and in this way you can prevent the backlash error example three in an instrument there are 25 divisions on the Vernier scale which have length of 24 divisions of the main scale one centimeter on Main scale is divided in 20 equal parts find the least count what is the value of one main scale division here value of 1 main scale division is equal to is given that one centimeter on Main scale is divided in 20 equal parts which means it will be 1 by 20 centimeter okay now what is the total number of Divisions on the Vernier scale in an instrument there are 25 divisions on Vernier scale it is directly given number of divisions on the Vernier skin n is equal to 25 okay this is represented as x x is 1 by 20 centimeter a number of divisions is 25 how to find the least count of a Vernier least count is equal to value of 1 Main scale division divided by number of Divisions on the Vernier scale so that is X by n 1 by 20 divided by 25 which is equal to 1 by 20 into 25 equal to 1 by 500 so what is 1 by 500 you will be getting 0.002 centimeters in centimeters it is 0.002 centimeter so this is the least count of the given instrument clear next example for the lease count of a Vernier calipers is 0.01 centimeter and 0 error is plus 0.02 centimeter while measuring the length of a road the main scale reading is 4.8 centimeter and 6 division on the Vernier scale is in line with the marking on the main scale calculate the length of the room so here we have to calculate the length of root so length of root will be equal to observed reading minus zero error so here the zero error is given yes okay about is the least count given the least count is equal to 0.01 centimeter then zero error is given 0 error the sign is very important here it is positive Sign Plus 0.02 centimeter okay first we need to find the observed reading what is observe reading observed reading foreign Plus least count at we have to determine the value that is here it is given that sixth division on Vernier scale is in line with the marking on the main scale so that is the coinciding value on the Vernier scale we are taking which you represented by P okay so P into least count so here the P value is 6 and LC these count we have 0.01 putting the values MSR mean scale Reading Main scale reading is given that is 4.8 plus p is 6 into least count to 0.01 which is equal to 4.8 plus 0.06 that is 4 point 8 6. centimeter okay so the observed reading is 4.86 centimeter now from this observed reading we will be subtracting the zero error to get the length of the root so length of root is equal to observed reading which is 4.86 minus 0 error that is 0.02 here it is positive sign okay we will be getting 4.84 centimeter which is the actual length of the root clear example 5 the circular head of a screw gauge is divided into 50 divisions and the screw moves one millimeter head in two revolutions of the circular head find its pitch and least curve okay here what is given number of divisions [Music] on circular head is equal to 50. okay it is given the distance moved distance mode in two revolutions is equal to one millimeter what is one millimeter it is 0.1 centimeter okay then what is the distance moved in one revolution distance moved in one revolution will give you the pitch pitch is equal to so the a part we have to find the pitch pitch is equal to distance mood in one revolution that is 0.1 centimeter divided by 2 which is equal to 0.05 centimeter if you need it in millimeter 0.5 millimeters okay now next we have to find the least count we know least count is equal to in case of a screw gauge please count is equal to pitch divided by number of divisions on circular head which is equal to pitch we have determined zero point zero five centimeter divided by number of Divisions on circular head what is the number of Divisions which is 50. 50 it is given in the question is equal to 5 divided by 5000 or 1 by 1000 equal to 0.001 centimeters if it is in centimeters you will get this value or 0.01 millimeters okay so this is your fine lines now let us do numericals from exercise 1B exercise 1B question one a stopwatch has 10 divisions graduated between the 0 and 5 Second marks what is its least count we have to find the least count here we have to find the range first okay range is equal to 0 and 5 Seconds Mark which means 5 Seconds minus zero seconds will give you the range that is equal to 5 Seconds okay then what is the total number of Divisions number of divisions is given number of divisions is equal to 10 how to find the least count least count will be equal to range divided by number of divisions which is equal to 5 seconds divided by 10 that is 0.5 seconds therefore the least count of the given stopwatch is equal to 0.5 seconds question 4 of exercise 1B a boy uses Vernier calipers to measure the thickness of his pencil he measures it to be 1.4 millimeter if the zero error of Vernier calipers is plus 0.02 centimeter what is the correct thickness of pencil how to get the correct thickness correct thickness will be equal to observed reading minus 0 error what is given in the question observed reading is given observe reading is equal to 1.4 millimeter what is the zero error zero error is equal to plus 0.02 centimeter so first thing you the unit should be same here it is in millimeter and here it is in centimeter either you have to convert this into centimeter or you have to convert this into millimeters okay what is 0.02 centimeter in millimeters you will be getting plus 0.2 millimeters okay now we can find the correct thickness correct thickness is equal to 1.4 millimeters minus the zero error which is 0.2 millimeter is equal to 1.2 millimeter okay so 1.2 millimeter is the correct thickness of the pencil question 9 of exercise 1B the pitch of a screw gauge is 0.5 millimeter and the head scale is divided in 100 Parts what is the least count of a screw gauge very simple question right we know the pitch is given which is equal to 0.5 millimeters number of Divisions on head scale is given number of divisions on circular head is equal to 100 to divide into 100 parts means the number of division will be 100 then the least count is equal to pitch divided by number of divisions on circular head which is equal to 0.5 millimeter divided by 100 equal to 0.00 5 millimeter if you have to convert it into centimeters 0.0005 centimeters just remember this thing one centimeter is 10 millimeters okay then one millimeter will be 1 by 10 centimeter here 0.05 0.005 millimeters will be equal to 0.005 by 10 centimeter which is 0.0005 centimeters clear that&amp;#39;s all for today in today&amp;#39;s class we have discussed how to measure length using screw gauge and Vernier calipers we have studied the parts of these we have also solved problems related to this from exercise one we hope you all enjoyed the session I&amp;#39;ll be back in the next session until then stay tuned to learn how free thank you

Transcript for:ICSE Class 9 Physics: Measurements and Experimentations - Chapter 1

Transcript for:
ICSE Class 9 Physics: Measurements and Experimentations - Chapter 1