Question

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

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

Answer 1

Answer: (B)

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

Energy stored per unit volume can be given as:

$E=\frac{1}{2}\times stress\times strain$ -----------(1)

From Hooke's law :

Young's modulus, $Y=\frac{Stress}{Strain}$

$⟹$ $Strain=\frac{Stress}{Y}=\frac{S}{Y}$ -----------(2)

From equation (1) and (2):

$\therefore$ $E=\frac{1}{2}\times S\times \frac{S}{Y}$

$\Rightarrow E=\frac{1}{2}\frac{S^2}{Y}$

Hence, the correct option is $\left(B\right)$