Mechanical Properties of Solids
141137
If $S$ is stress and $Y$ is Young's modulus of a material of wire, then energy stored in the wire per unit volume is:
1 $2 \mathrm{~S}^{2} \mathrm{Y}$
2 $\frac{\mathrm{S}}{2 \mathrm{Y}}$
3 $\frac{2 \mathrm{Y}}{\mathrm{S}^{2}}$
4 $\frac{S^{2}}{2 Y}$
Explanation:
D Given that, Young's modulus $=$ Y, stress $=\mathrm{S}$
Energy stored per unit volume $=\frac{1}{2} \times$ stress $\times$ strain
$\mathrm{E}=\frac{1}{2} \times \mathrm{S} \times \frac{\mathrm{S}}{\mathrm{Y}} \quad\left(\because \text { strain }=\frac{\text { stress }}{\mathrm{Y}}\right)$
$\mathrm{E}=\frac{\mathrm{S}^{2}}{2 \mathrm{Y}}$