PYQ NEET- Units Of Measurement L-4

Question: A metal wire has mass $(0.4 \pm 0.002) \mathrm{g}$, radius $(0.3 \pm 0.001) \mathrm{mm}$ and length $(5 \pm 0.02) \mathrm{cm}$. The maximum possible percentage error in the measurement of density will nearly be :#

A) $1.3 %$

B) $1.6 %$

C) $1.4 %$

D) $1.2 %$

Answer: $1.6 %$#

Solution:#

$$ \begin{aligned} & \rho=\frac{M}{V} \ & \rho=\frac{M}{\pi r^2 \ell} \ & \frac{\Delta \rho}{\rho}=\frac{\Delta \mathrm{M}}{\mathrm{M}}+\frac{2 \Delta \mathrm{r}}{\mathrm{r}}+\frac{\Delta \ell}{\ell} \ & \frac{\Delta \rho}{\rho} %=\left[\frac{0.002}{0.4}+\frac{2(0.001)}{(0.3)}+\frac{0.02}{5}\right] \times 100 % \ & =\frac{1}{2} %+\frac{2}{3} %+\frac{2}{5} % \ & =1.6 % \end{aligned} $$