00:01
In this problem we are given this square, it can be some object, and we are measuring the side length, let's call it l, to be 20 centimeters with a possible error of 0 .03 centimeters.
00:19
So 20 plus minus 0 .03 centimeters is the side length of this square.
00:29
Using this information we are going to do some tiny error in two different parts of this problem.
00:38
In the first part we are going to compute the percent error in the area of this square object.
00:46
Okay, let's call the area a.
00:48
So we have a equal to s squared and the uncertain or the error in area is given by the square root the partial derivative of the area with respect to the first parameter which is l and which is the only parameter in fact in this problem times the uncertainty in this parameter this is squared so if we had some other parameters of course we would add them over here with by taking individual partial derivatives but since we have only one parameter this is sufficient for our case.
01:32
Okay, so we have the absolute value partial a or partial l times delta and partial partial a or partial l is just two times l and since l and delta l are positive quantities we can directly write delta a equal to two times l times delta l okay now let's compute this numerically we have two times 20 times 0 .03 so this is 1 .2 centimeter squared but we don't want this we want the percent error percent error with respect to no area itself so we will take this error divide by the actual area or the central value of the area and we'll multiply it by 100%.
02:35
So we get 1 .2 divide by 20 squared times 100 % and this turns out to be 0 .3%.
02:47
So this is the percent error in the area.
02:53
Now let's do the other part.
02:57
We will carry out the same exact calculation but in the opposite direction because now in this part we are given this maximum allowable percent error in the area so we are going in the opposite direction if this maximum percent error in the area is 2 .1 percent the question is what is the allowed, again maximum error in the side length measurement? so there's the question.
03:40
But of course we are going to simply calculate delta l, we will compute it as percentage.
03:48
Okay, so using this we have delta a equal to 2 .1 divided by 100 times a...