Question

If in a wire of Young's modulus $Y$, longitudinal strain $X$ is produced, then the elastic potential energy stored in its unit volume will be

• A. $2Y{X}^2$
• B. $0.5Y{X}^2$
• C. $0.5Y^{2}X$
• D. $Y{X}^2$

Answer 1

The correct option is B $0.5Y{X}^2$

Elastic Potential energy per unit volume is given by
$U=\frac{1}{2}\times \text{stress}\times \text{strain}$
$U=\frac{1}{2}\times Y\times (\text{strain}{)}^2$
$(\because \text{stress}=Y\times \text{strain})$
$\therefore U=\frac{1}{2}{X}^{2}Y$
$\Rightarrow U=0.5X^{2}Y$