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

The volume of the wire is given by, $V=\pi r^{2}L$

Thus density of the wire, $\rho =\frac{m}{\pi r^{2}L}$

Taking log and then differentiate:

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

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

$⟹$ Percentage error in density is $4$%.