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)

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