Physics - Error Question with Solution | TestHub

Volume of the wire is $V=\pi r^{2}l$.

Density of the wire is $\rho =\frac{m}{\pi r^{2}l}$

Relative error in measurement of density

$\Rightarrow \frac{\Delta \rho }{\rho }=\frac{\Delta m}{m}+2\times \frac{\Delta r}{r}+\frac{\Delta l}{l}$

$=\frac{0.006}{0.6}+2\times \frac{0.005}{0.5}+\frac{0.04}{4}$

$=0.01+0.02+0.01=0.04$

$\therefore$ Percentage error in $\rho =0.04\times 100=4\%$