Question

When an elastic material with Young's modulus Y is subjected to stretching stress S, elastic energy stored per unit volume of the material is

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

Answer 1

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

Given,

Young's modulus $=Y,$

Streaching stress$=S,$

Energy stored per unit volume is, $=\frac{1}{2}\times$ stress $\times$ strian

We know that, stress $=$ strain $\times Y$

Therefore energy per unit volume will be $E=\frac{1}{2}\times S\times \frac{S}{Y}=\frac{S^2}{2Y}$

Therefore option $C$ is correct.