Question

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

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

Answer 1

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

Elastic potential energy per unit volume

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

=$\frac{1}{2}\times$ [Young's modulus $\times$ strain] $\times$ strain

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