Physics - Elasticity Question with Solution | TestHub

Given: $Y=2\times 10^{11}{\mathrm{Nm}}^{-2}$, Stress $=5\times 10^7{\mathrm{Nm}}^{-2}$, $\frac{\Delta V}{V}=0.02\%=2\times 10^{-4}$.

Longitudinal strain, $\frac{\Delta L}{L}=\frac{Stress}{Y}=\frac{5\times 10^7}{2\times 10^{11}}=2.5\times 10^{-4}$.

For a wire, $V=\pi r^{2}L$.

Taking the differential, $\frac{\Delta V}{V}=\frac{2\Delta r}{r}+\frac{\Delta L}{L}$.

$2\times 10^{-4}=\frac{2\Delta r}{r}+2.5\times 10^{-4}$.

$\frac{2\Delta r}{r}=2\times 10^{-4}-2.5\times 10^{-4}=-0.5\times 10^{-4}$.

$\frac{\Delta r}{r}=-0.25\times 10^{-4}$.

The fractional decrease in radius is $0.25\times 10^{-4}$.