JEE Advanced 2024 · Paper 2 · Physics Q8

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PhysicsInteger+4Question 25 of 51

The dimensions of a cone are measured using a scale with a least count of $2\,\mathrm{mm}$ . The diameter of the base and the height are both measured to be $20.0\,\mathrm{cm}$ . The maximum percentage error in the determination of the volume is _____.

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Answer and worked solution

Official answer: 3

$V=\frac13\pi r^2h=\frac{\pi d^2h}{12}$ . The maximum relative error is
$\frac{\Delta V}{V}=2\frac{\Delta d}{d}+\frac{\Delta h}{h}=2\cdot\frac{0.2}{20}+\frac{0.2}{20}=0.03,$
i.e. $3\%$ .

Topics:Errors in measurement Least count

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