Question

A metallic wire is stretched by suspended weight to it. If $\alpha$ is the longitudinal strain and $Y$ its Young’s modulus of elasticity, elastic potential energy per unit volume is

• A. $Y{\alpha }^2$
• B. $\frac{1}{2}Y{\alpha }^2$
• C. $\frac{3}{2}Y{\alpha }^2$
• D. $\frac{Y}{{\alpha }^2}$

Answer 1

Answer: (B)

Elastic energy per unit volume
$=\frac{1}{2}\times stress\times strain$
Here, strain $=\alpha ,$
$=$and $Y=\frac{stress}{strain}orstress=Y\times strain$
$\therefore stress=Y\times \alpha$
Elastic energy per unit volume
$=\frac{1}{2}\times (Y\times \alpha )\times \alpha =\frac{1}{2}Y{\alpha }^2$