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MHT CET 2026 (13 Apr, Shift 2) · Errors in Measurement

Errors in Measurement question from MHT CET 2026 (13 Apr, Shift 2)

Q27MHT CET 2026 · 13 APR · SHIFT 2Medium

Errors in Measurement

The length of a cylinder is measured with a meter rod having least count $0.1$ cm. Its diameter is measured with vernier calipers having least count $0.01$ cm. Length of cylinder is $8.0$ cm and radius is $4.0$ cm. Find the percentage error in the calculated value of the volume.

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Answer: (c)

$V = \frac{\pi d^2 l}{4}$ , so $\frac{\Delta V}{V} = 2\frac{\Delta d}{d} + \frac{\Delta l}{l}$
Diameter $d = 8.0$ cm, so $\frac{\Delta d}{d} = \frac{0.01}{8.0} = 0.125\%$ ; $\frac{\Delta l}{l} = \frac{0.1}{8.0} = 1.25\%$
$\frac{\Delta V}{V} = 2(0.125\%) + 1.25\% = 1.5\%$
So the answer is (c) $1.5\%$ .

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