Question

A elastic material of young's modulus $Y$ is subjected to a stress $S$. The elastic energy stored per unit volume of the material is

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

Answer 1

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

Energy per unit volume $=\frac{1}{2}\times Stress\times Strain$
$=\frac{1}{2}\times Stress\times \frac{Stress}{Y}|Y=\frac{Stress}{Strain}=\frac{S^2}{2Y}$.