Question

An 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 $\frac{S^2}{2Y}$

Stress is represented by, $S$

From Hooke's law : $Y=\frac{Stress}{Strain}$

$⟹$ $Strain=\frac{Stress}{Y}=\frac{S}{Y}$ ...........(1)

Elastic energy per unit volume : $E_v=\frac{1}{2}\times Stress\times Strain$

$\therefore$ $E_v=\frac{1}{2}\times S\times \frac{S}{Y}=\frac{S^2}{2Y}$ (using (1))