Question

A metallic wire is stretched by suspending a weight to it. If ${\alpha }^2$ is the longitudinal strain and Y is its Young's modulus of elasticity , then show that the elastic potential energy per unit volume is given by 1/2 $Y^2.$

Answer 1

$E=\frac{1}{2}\times stress\times strain$

$=\frac{1}{2}\times Y{\alpha }^2\times {\alpha }^2$

$=\frac{1}{2}{Y\alpha }^4$.