Question

The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and lengths are $3\%$ and $2\%$ respectively. The maximum $\%$ error in the measurement of density would be

• A. $12\%$
• B. $9\%$
• C. $14\%$
• D. $7\%$

Answer 1

The correct option is B $9\%$

Given that
$\frac{\Delta m}{m}\times 100=3\%$ and $\frac{\Delta l}{l}\times 100=2\%$
From formula,
for the volume of cube $\left(V\right)=l^3$ and
density $\left(\rho \right)$ = $\frac{\text{mass}\left(m\right)}{\text{volume}\left(V\right)}=\frac{m}{l^3}$
For maximum $\%$ error in density measurement,
$\frac{\Delta \rho }{\rho }=\frac{\Delta m}{m}+3\frac{\Delta l}{l}$
$\Rightarrow \frac{\Delta \rho }{\rho }\times 100=(\frac{\Delta m}{m}+\frac{3\Delta l}{l})\times 100$
$=3+(3\times 2)=9\%$
So $\%$ error in density = 3 + 3(2) = 9%.
Hence, option $\left(d\right)$ is the correct answer.