A metal wire has mass (0.4 ± 0.002) g, radius (0.3 ± 0.001) mm and length (5 ± 0.02) cm. The maximum possible percentage error in the measurement of density will nearly be: (a) 1.3% (b) 1.6% (c) 1.4% (d) 1.2%

Answer: (b). ρ = (m)/(π r² l), so (Δρ)/(ρ) = (Δ m)/(m) + 2(Δ r)/(r) + (Δ l)/(l) = (0.002)/(0.4) + 2·(0.001)/(0.3) + 0.02/5 = 0.5% + 0.67% + 0.4% (Δρ)/(ρ) ≈ 1.57% ≈ 1.6% So the answer is (b) 1.6%.

A metal wire has mass (0.4 ± 0.002) g, radius (0.3 ± 0.001) mm and… | NEET 2023

Q68NEET 2023Easy

Errors in Measurement

A metal wire has mass $(0.4 \pm 0.002)\text{ g}$ , radius $(0.3 \pm 0.001)\text{ mm}$ and length $(5 \pm 0.02)\text{ cm}$ . The maximum possible percentage error in the measurement of density will nearly be:

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Answer: (b)

$\rho = \frac{m}{\pi r^2 l}$ , so $\frac{\Delta\rho}{\rho} = \frac{\Delta m}{m} + 2\frac{\Delta r}{r} + \frac{\Delta l}{l}$
$= \frac{0.002}{0.4} + 2\cdot\frac{0.001}{0.3} + \frac{0.02}{5} = 0.5\% + 0.67\% + 0.4\%$
$\frac{\Delta\rho}{\rho} \approx 1.57\% \approx 1.6\%$
So the answer is (b) 1.6%.

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