 So similarly you know just like we have talked about length right we talked about how to calculate the bigger length how to estimate the smaller distances similarly masses also there are methods to calculate the big mass there are methods to estimate the smaller mass okay the kind of mass we are dealing with is this you know the smallest mass could be the mass of the electron okay so the size we are dealing with with respect to mass is the mass of one electron and the range of mass could go up to let us say from electron the mass of the observable universe is 10 square 55 kgs okay indirectly you can find milky way galaxy mass is roughly 10 square 41 kgs okay so 10 square 55 kg is roughly the mass of the universe okay so we are dealing with a huge range 10 square minus 31 till 10 square 55 kgs and there cannot be a direct method to measure the mass of electron you can push you can put a electron over here and put a bar over here okay fine electron is this much okay there has to be some indirect method the way we have derived the lengths using the definition of angles and using such experiments there are some indirect method to calculate the mass also okay for example the method to estimate the mass of the earth you know that earth will revolve around the sun in 365 days so just by using that information you can calculate the mass of the earth okay there are ways we'll talk about in gravitation chapter oh using the angular yeah so yeah okay the humans mass is given as 100 kgs here anyways so we are not getting into details of how to measure indirectly the mass I'm just telling you we have we have introduced how to measure indirectly the length similarly there are cases to measure the mass indirectly and likewise there are method to measure the time also okay now the range of the time we are dealing with is this you can talk about let's say the ratio of longest to the shortest time interval we're dealing with is a about 10 is for 41 okay so the range is huge okay so you cannot use clock every time to measure the time also by the time you measure the time you yourself have grown and died out getting it you can't put a clock and start measuring okay fine let me sit here and measure the time itself all right so that is why these indirect methods are very very important okay so this is with respect to the measurement of length measurement of mass and measurement of time okay next we're not getting into the measurement of other fundamental quantities but next we are talking about some of the very important aspects of the measurement whenever you measure anything there is always used to be an error associated with the measurement yes or no yeah why do you think you are taking multiple measurements in the lab because you don't know what is the exact value you don't know so you what you're doing is okay fine let me take the multiple measurement then i'll take the mean of it and i'll say that is my roughly closer to the value okay and why do you think you have steps of conducting experiment step number one check this step number two do that step number three you write the record right step by step you write step one step two step three which is very boring thing to do but why you have to do it in that manner to prevent to prevent the systematic errors for example if we we have always this habit of let let us say we all the time we ignore the zero error you know what is the zero error you don't know suppose suppose we have this hat habit of looking at things like this okay then we'll have parallax error for example if this is the let's say this is the pointer this is the scale on which i have to measure something if suppose i have to see where this chalk related to the scale so if i have this habit of measuring like i feel as if chalk is coinciding with this mark so i'll say this is the length and if i if i have this habit of looking from there the chalk will coincide from here so i'll say this is the length okay these kind of errors can be removed easily if you follow step by step manner of doing the experiment there will be one step where you have to be like looking at it right from the above don't look at sideways things like that okay these are the precautions which you have to do all right so these errors which you can remove you remove it by step by step conduction of the experiment okay but there are few errors which you cannot remove okay so there will be error all right let's talk about the errors little bit so whenever we talk about errors there are two kinds of errors okay write down okay that now i have to start asking you to get out random and systematic okay now have you heard of these terms accuracy and precision what is the difference same thing same thing so why two words she's correct in a way precision and accuracy i'll give you one example you tell me what is precise and what is accurate or we can say what is not precise and what is not accurate here i here is the first example there is a student who always get 27 marks out of 30 in their school ut always okay and the kind of error this person does suppose seven chapters are asked he does in first ut he he made an error in chapter number one second ut he made an error in chapter number three third ut chapter number four next ut chapter number five other ut chapter number seven are you getting it so these kind of errors he's making but he made sure that only three marks are gone and he's getting 27 out of 30 again and again okay this is example number one example two is also a student who is getting 27 out of 30 but he's always making error in let us say calculating the distance using parallax method unit one same error unit two same error unit three same error four till all the ut is making this error getting it now tell me which is which you can correct easily first one or second one second one second one you exactly know where is the problem you'll correct it and he'll start getting 30 out of 30 okay what about the first person you can't do anything it is in his blood you get 27 out of 30 no the thing is that aja we're talking about accuracy and precise who is more precise in getting 27 out of 30 both are the precision aja tell me who is more precise in making error second who is who is very accurate in measuring in making the error okay you have not understood okay let me give you another example guys let me give you another example here is you've you've played the dart ball this is your bingo okay and there are two players okay this is one and this is another dart ball okay now player number one is scoring like this this is player number one okay player number two is this who has precision but not accuracy who is precise and who is accurate second one is precise first one is accurate so now tell me what is the difference between accurate and precise accuracy is closer to the accuracy is closer to the true value and precise means precise means the same value is getting repeated precisely okay now which player you want one or two huh why why would you want to if you aim once at the center you're always going to get the same but you can't aim at the center that's why he's getting those okay how many of you want player one okay how many of you want player one only one person you also want player one not accuracy yes player two almost everybody else okay so of course there's a reason why player two is making this error there's a reason understood but there's no reason why player is doing this player one is doing this are you getting my point maybe player two is aiming from one eye only and if you tell okay listen you have to aim from both the eyes and start getting once he start getting it here then he is beating player one hands down are you getting it he has to just shift this in this direction of it are you getting it okay player one very difficult to improve precise can become accurate very easily but accuracy cannot guarantee your precision I'll give you one more example suppose you have two clocks okay clock number one suppose you are taking reading when it is exactly 12 when it is exactly 12 you're taking readings of the two clocks okay clock number one reading is like this 12 o 5 11 50 12 o 7 11 55 this is the reading of clock one okay every day at 12 noon these are the readings of the clock one clock two this is the reading 10 10 9 59 10 4 1 which one you want clock to decide to you're good clock two you just have to rotate it a little bit put the hour and at 12 when it is 12 are you getting it but you can't improve this understood more precise more accurate precision always trumps the accuracy so but uh if when accuracy tends towards the like the the true value doesn't it become more precise like if you add your player one yeah so if he got closer and yeah if player one is like this then he's both accurate and precise then there's nothing to improve on okay so keep this in mind the difference between accuracy and precision