Question

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

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

Answer 1

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

Potential energy stored per unit volume of a wire
$=\frac{1}{2}\times \text{Stress}\times \text{strain}$
$=\frac{1}{2}\times Y\times X\times X[\text{Stress}=Y\times X]$
$=0.5Y{X}^2$