A cylindrical wire of mass (0.4 ± 0.01) g has length (8 ± 0.04) cm and radius (6 ± 0.03) mm. The maximum error in its density will be: (a) 1% (b) 5% (c) 4% (d) 3.5%

Answer: (c). ρ = (m)/(π r² l), so (Δρ)/(ρ) = (Δ m)/(m) + 2(Δ r)/(r) + (Δ l)/(l) = (0.01)/(0.4) + 2·0.03/6 + 0.04/8 = 2.5% + 1% + 0.5% So the answer is (c) 4%.

A cylindrical wire of mass (0.4 ± 0.01) g has length (8 ± 0.04) cm… | JEE Main 2023 (8 Apr, Shift 1)

Q70JEE Main 2023 · 8 APR · SHIFT 1Easy

Errors in Measurement

A cylindrical wire of mass $(0.4 \pm 0.01)\text{ g}$ has length $(8 \pm 0.04)\text{ cm}$ and radius $(6 \pm 0.03)\text{ mm}$ . The maximum error in its density will be:

Show answer and solution

Answer: (c)

$\rho = \frac{m}{\pi r^2 l}$ , so $\frac{\Delta\rho}{\rho} = \frac{\Delta m}{m} + 2\frac{\Delta r}{r} + \frac{\Delta l}{l}$
$= \frac{0.01}{0.4} + 2\cdot\frac{0.03}{6} + \frac{0.04}{8} = 2.5\% + 1\% + 0.5\%$
So the answer is (c) 4%.

Report a mistake

More questions on Errors in Measurement

A physical quantity P is given as P = a² b³c√(d) The percentage error in the measurement…JEE Main 2023 (10 Apr, Shift 1)
The percentage error in the measurement of g is: (Given that g = (4π² L)/(T²), L = (10 ±…NEET 2022 (Phase 2)
A silver wire has a mass (0.6 ± 0.006) g, radius (0.5 ± 0.005) mm and length (4 ± 0.04)…JEE Main 2022 (27 Jun, Shift 1)
If Z = (A²B³)/(C⁴), then the relative error in Z will be:JEE Main 2022 (25 Jun, Shift 1)
A torque meter is calibrated to reference standards of mass, length and time each with 5%…JEE Main 2022 (27 Jul, Shift 1)
The maximum error in the measurement of resistance, current and time for which current…JEE Main 2022 (25 Jul, Shift 2)
For z = a² x³ y1/2, where 'a' is a constant. If percentage error in measurement of 'x'…JEE Main 2022 (25 Jun, Shift 2)
In an experiment to find acceleration due to gravity (g) using simple pendulum, time…JEE Main 2022 (28 Jul, Shift 2)

Errors in Measurement question from JEE Main 2023 (8 Apr, Shift 1)

More questions on Errors in Measurement