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

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

A wire has a mass 0.3 ± 0.003 gram, radius 0.5 ± 0.005 mm and length… | MHT CET 2025 (25 Apr, Shift 1)

Q40MHT CET 2025 · 25 APR · SHIFT 1Easy

Errors in Measurement

A wire has a mass $0.3 \pm 0.003$ gram, radius $0.5 \pm 0.005\text{ mm}$ and length $6 \pm 0.06\text{ cm}$ . The maximum percentage error in the measurement of its density is

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Answer: (c)

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

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