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
IIT 1992,AIIMS 1997,AIEEE 2005, Easy
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(b) 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
$E=\frac{1}{2} \times S \times \frac{S}{Y}=\frac{S^{2}}{2 Y}$
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