The amount of elastic potential energy per unit volume (in SI unit) of a steel wire of length $100…
The amount of elastic potential energy per unit volume (in SI unit) of a steel wire of length $100 \mathrm{~cm}$ to stretch it by $1 \mathrm{~mm}$ is (if Young's modulus of the wire $=2.0 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$ )
$10^7$
$10^5$
$10^{11}$
$10^{17}$
Solution
We know that, elastic potential energy per unit volume $=\frac{1}{2} \times$ Stress $\times$ Strain
Also, $Y=\frac{\text { Stress }}{\text { Strain }}$
$\Rightarrow \quad$ Elastic potential energy per unit volume $=\frac{1}{2} \times$ Young's modulus $\times(\text { Strain })^2$
$\begin{aligned} & =\frac{1}{2} \times 2 \times 10^{11} \times\left[\frac{1}{1000}\right]^2 \\ & =\frac{1}{2} \times 2 \times 10^{11} \times 10^{-6}=10^5\left(\mathrm{~J} / \mathrm{m}^3\right)\end{aligned}$