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I'm supposed to come up with a way to measure the thickness of paper. I've come up with the following approach.

Let us suppose we have a paper of thickness $?$, length $a$, breadth $b$, density $\rho$. Let us say I use an Analytical Balance to measure the mass of the paper and it comes out to be $m$. Then I can use the formula for density and volume to come up with the thickness of that paper: $$\rho=\dfrac{m}{V}=\dfrac{m}{?ab}\implies ?=\dfrac{m}{\rho ab}$$

Now this looks valid because if I shorten the paper's dimensions, that does not change it's thickness but indeed changes it's mass such that the thickness remains constant. Is this a good approach? Any suggestions are appreciated. Thanks

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    $\begingroup$ How accurately do you know $\rho$? $\endgroup$ – The Photon Apr 28 at 14:42
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    $\begingroup$ This is a fine approach assuming the paper is fairly even in thickness. And of course assuming that you know the density. $\endgroup$ – Steeven Apr 28 at 14:52
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Use a ruler. Stack several reams on a desk, measure the height, and divide the total height by the number of sheets in the stack.

You want to use a big stack because the error in your result for a single sheet equals the error in the stack height measurement divided by the number of sheets.

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The difficulty of the problem is that the thickness of the paper is too small with the usual apparatus we use in our homes for typical measurements. One approach could be to take an amount of 100 paper sheets and press them until there is no air between them. Then measure the total thickness as accurately as you can and divide the result by 100.

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  • $\begingroup$ This is a good improvement on the initial method. Thanks :) $\endgroup$ – Paras Khosla Apr 28 at 15:14

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