Question

A wire has a mass (0.4 ± 0.004) g, radius (0.6+ 0.006) mm and length (7 ± 0.07) cm. The maximum percentage error in the measurement of its density is ______.

पर्याय

• 4

• 2

• 3

• 1

Answer 1

A wire has a mass (0.4 ± 0.004) g, radius (0.6+ 0.006) mm and length (7 ± 0.07) cm. The maximum percentage error in the measurement of its density is 4.

Explanation:

\[\mathrm{Here},\frac{\Delta m}{m}=\frac{0.004}{0.4},\frac{\Delta r}{r}=\frac{0.006}{0.6},\frac{\Delta L}{L}=\frac{0.07}{7}\]
\[\begin{aligned} & & & \mathrm{As~p}=\frac{\mathrm{m}}{(\mathrm{mr}^{2})\mathrm{L}}, \\ & \therefore & & \left({\frac{\Delta\rho}{\rho}}\right)\times100=\left({\frac{\Delta m}{m}}+{\frac{2\Delta r}{r}}+{\frac{\Delta L}{L}}\right)\\ & & & =\left(\frac{0.004}{0.4}+\frac{2\times0.006}{0.6}+\frac{0.07}{7}\right)\times100 \\ & & & =1+2+1=4\% \end{aligned}\]