Question

A sliver wire has 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 :

• A. $4 \%$
• B. $3 \%$
• C. $6 \%$
• D. $7 \%$

Answer 1

Answer: (A)

$M=(0.6 \pm 0.006) g$
$r=(0.5 \pm 0.005) mm$
$l=(4 \pm 0.04) cm$
$\rho=\frac{m}{V}$
$\Rightarrow \frac{\Delta \rho}{\rho}=\frac{\Delta m}{m}+\frac{2 \Delta r}{r}+\frac{\Delta l}{l}$
$\left(\right.$ Volume of cylinder $\left.=\pi r^{2} l\right)$
$=\frac{0.006}{0.6}+\frac{2 \times 0.005}{0.5}+\frac{0.04}{4}$
$100 \times \frac{\Delta \rho}{\rho}=4 \times 10^{-2} \times 100$
$\frac{\Delta \rho}{\rho} \times 100=4 \%$