Question

A wire has a mass$(0.3\pm 0.003)g$, radius $(0.5\pm 0.005)mm$ and length $(6\pm 0.06)cm$. The maximum percentage error in the measurement of its density is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is D $4$

Density $\rho =\frac{m}{\pi r^{2}L}$

$\frac{\Delta \rho }{\rho }\times 100=[\frac{\Delta m}{m}+2\frac{\Delta r}{r}+\frac{\Delta L}{L}]\times 100$

$\frac{\Delta \rho }{\rho }\times 100=[\frac{0.003}{0.3}+2\frac{0.005}{0.5}+\frac{0.06}{6}]\times 100\frac{\Delta \rho }{\rho }\times 100=4\%$