Question

If $S$ is stress and $Y$ is Young's modulus of the material of a wire, the energy stored in the wire per unit volume is

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

Answer 1

Answer: (B)

Energy stored in the wire $=\frac{1}{2}$ stress $\times$ strain $\times$ volume
and Young's modulus $=\frac{\text { Stress }}{\text { Strain }}$
$\Rightarrow$ strain $=\frac{S}{Y}$
$\frac{\text { Energy stored in wire }}{\text { Volume }}=\frac{1}{2} \times$ stress $\times$ strain
$=\frac{1}{2} S \times \frac{S}{Y}=\frac{S^{2}}{2 Y}$