Question

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

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

Answer 1

Answer: (D)

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

Answer 2

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