A silver wire has a mass (0.6 ± 0.006) g, radius (0.5 ± 0.005) mm and length (4 ± 0.04) cm. The maximum percentage error in the measurement of its density will be: (a) 4% (b) 3% (c) 6% (d) 7%

Answer: (a). ρ = (m)/(π r² l), so (Δρ)/(ρ) = (Δ m)/(m) + 2(Δ r)/(r) + (Δ l)/(l) = (0.006)/(0.6) + 2·(0.005)/(0.5) + 0.04/4 = 1% + 2% + 1% So the answer is (a) 4%.

A silver wire has a mass (0.6 ± 0.006) g, radius (0.5 ± 0.005) mm and… | JEE Main 2022 (27 Jun, Shift 1)

Q73JEE Main 2022 · 27 JUN · SHIFT 1Easy

Errors in Measurement

A silver wire has a mass (0.6 $\pm$ 0.006) g, radius (0.5 $\pm$ 0.005) mm and length (4 $\pm$ 0.04) cm. The maximum percentage error in the measurement of its density will be:

Show answer and solution

Answer: (a)

$\rho = \frac{m}{\pi r^2 l}$ , so $\frac{\Delta\rho}{\rho} = \frac{\Delta m}{m} + 2\frac{\Delta r}{r} + \frac{\Delta l}{l}$
$= \frac{0.006}{0.6} + 2\cdot\frac{0.005}{0.5} + \frac{0.04}{4} = 1\% + 2\% + 1\%$
So the answer is (a) 4%.

Report a mistake

Errors in Measurement question from JEE Main 2022 (27 Jun, Shift 1)

More questions on Errors in Measurement