In the density measurement of a cube, the mass and edge length are measured as $(10.00 \pm 0.10) \mathrm{kg}$ and $(0.10 \pm 0.01) \mathrm{m}$, respectively. The error in the measurement of density is:

(B) $0.31 \mathrm{~kg} / \mathrm{m}^{3}$

(A) $0.10 \mathrm{~kg} / \mathrm{m}^{3}$

(C) $0.07 \mathrm{~kg} / \mathrm{m}^{3}$

(D) $0.01 \mathrm{~kg} / \mathrm{m}^{3}$

JEE Main · 2019 · 09 Apr 2019 · Shift 1 · Units & Measurement

In the density measurement of a cube, the mass and edge length are measured as

(10.00 \pm 0.10) kg

and

(0.10 \pm 0.01) m

, respectively. The error in the measurement of density is:

Answer: (B)

For

ρ = m / L^{3}

, the relative error is

\frac{Δ ρ}{ρ} = \frac{Δ m}{m} + 3 \frac{Δ L}{L} = \frac{0.10}{10.00} + 3 \times \frac{0.01}{0.10} = 0.01 + 0.30 = 0.31

. The intended answer is this relative error,

0.31

(option B); the 'kg/m^3' unit shown on the options is a transcription artefact (the absolute error would be

0.31 \times 1 0^{4} = 3.1 \times 1 0^{3} kg/ m^{3}

JEE Main · 2019 · 09 Apr 2019 · Shift 1 · Single correct option