Question

A wire has a mass $0.4\pm0.004\, g$ and length $8\pm0.08\left(cm\right)$ The maximum percentage error in the measurement of its density is $4\%$. The radius of the wire is $r\pm\Delta r$ find $\Delta r$

• A. 0.02 r
• B. 0.01 r
• C. 0.03 r
• D. 0.1 r

Answer 1

Answer: (B)

$\rho=\frac{m}{\pi r^{2}L}$
$\frac{\Delta\rho}{\rho}\times100=\left[\frac{\Delta m}{m}+2\frac{\Delta r}{r}+\frac{\Delta L}{L}\right]\times100$
$=\left(0.01+2\frac{\Delta r}{r}+0.01\right)\times100=4 \left(given\right)$
or $100\frac{\Delta r}{r}=1$
$\Delta r=0.01\,r$