A wire has mass (0.3 ± 0.003) gram, radius (0.5 ± 0.005) cm and length (6 ± 0.06) cm. The maximum percentage error in the measurement of density is (a) 2 % (b) 3 % (c) 4 % (d) 5 %

Answer: (c). ρ = mπ r² l ⇒ (Δρ)/(ρ) = (Δ m)/(m) + 2(Δ r)/(r) + (Δ l)/(l) = (0.003)/(0.3) + 2·(0.005)/(0.5) + 0.06/6 = 1% + 2% + 1% So the answer is (c) 4%.

A wire has mass (0.3 ± 0.003) gram, radius (0.5 ± 0.005) cm and… | MHT CET 2026 (16 Apr, Shift 1)

Q14MHT CET 2026 · 16 APR · SHIFT 1Easy

Errors in Measurement

A wire has mass $(0.3 \pm 0.003)$ gram, radius $(0.5 \pm 0.005)$ cm and length $(6 \pm 0.06)$ cm. The maximum percentage error in the measurement of density is

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Answer: (c)

$\rho = \frac{m}{\pi r^{2} l} \Rightarrow \frac{\Delta\rho}{\rho} = \frac{\Delta m}{m} + 2\frac{\Delta r}{r} + \frac{\Delta l}{l}$
$= \frac{0.003}{0.3} + 2\cdot\frac{0.005}{0.5} + \frac{0.06}{6} = 1\% + 2\% + 1\%$
So the answer is (c) $4\%$ .

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