A wire has mass (0.4 ± 0.002) g, radius (0.6 ± 0.006) mm and length (8 ± 0.04) cm. The percentage error in the measurement of its density is (a) 2% (b) 2.55% (c) 3% (d) 3.55%

Answer: (c). ρ = mπ r² l ⇒ (Δρ)/(ρ) = (Δ m)/(m) + 2(Δ r)/(r) + (Δ l)/(l) = (0.002)/(0.4) + 2·(0.006)/(0.6) + 0.04/8 = 0.5% + 2% + 0.5% So the answer is (c) 3%.

A wire has mass (0.4 ± 0.002) g, radius (0.6 ± 0.006) mm and length… | MHT CET 2026 (19 May, Shift 2)

Q4MHT CET 2026 · 19 MAY · SHIFT 2Easy

Errors in Measurement

A wire has mass $(0.4 \pm 0.002)$ g, radius $(0.6 \pm 0.006)$ mm and length $(8 \pm 0.04)$ cm. The percentage error in the measurement of its density is

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Answer: (c)

$\rho = \frac{m}{\pi r^{2} l} \Rightarrow \frac{\Delta\rho}{\rho} = \frac{\Delta m}{m} + 2\frac{\Delta r}{r} + \frac{\Delta l}{l}$
$= \frac{0.002}{0.4} + 2\cdot\frac{0.006}{0.6} + \frac{0.04}{8} = 0.5\% + 2\% + 0.5\%$
So the answer is (c) $3\%$ .

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Errors in Measurement question from MHT CET 2026 (19 May, Shift 2)

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