Question

If a wire stretched by hanging a weight from its end, the elastic potential energy per unit volume in terms of longitudinal strain $\sigma$ and modulus of elasticity $Y$ is :-

• A. $\frac{Y\sigma }{2}$
• B. $\frac{Y{\sigma }^2}{2}$
• C. $\frac{2Y{\sigma }^2}{2}$
• D. $\frac{Y^2\sigma }{2}$

Answer 1

The correct option is B $\frac{Y{\sigma }^2}{2}$

Energy density $=\frac{1}{2}\times \text{stress}\times \text{strain},$

$Y=\frac{\text{stress}}{\sigma }\text{or stress}=Y\sigma$
$\therefore \text{Energy density}=\frac{1}{2}Y\sigma \times \sigma =\frac{Y{\sigma }^2}{2}$

Hence, option (a) is the correct answer.