In the density measurement of a cube,
Question:

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:

1. (1) $0.01 \mathrm{~kg} / \mathrm{m}^{3}$

2. (2) $0.10 \mathrm{~kg} / \mathrm{m}^{3}$

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

4. (4) $0.07 \mathrm{~kg} / \mathrm{m}^{3}$

Correct Option: 3

Solution:

(3) $d=\frac{M}{V}=\frac{M}{L^{3}}=M L^{-3}$

$\frac{\Delta d}{d}=\frac{\Delta M}{M}+3 \frac{\Delta L}{L}$

$=\frac{0.10}{10.00}+3\left(\frac{0.01}{0.10}\right)=0.31 \mathrm{kgm}^{-3}$