Question

Young's modulus of the material of a wire is Y. If it is under a stress S, the energy stored per unit volume is given by:

• A. $\frac{1}{2}\frac{S}{Y}$
• B. $\frac{1}{2}\frac{S^2}{Y}$
• C. $\frac{1}{2}\frac{S}{Y^2}$
• D. $\frac{1}{2}\frac{S^2}{Y^2}$

Answer 1

Answer: (B)

$\frac{1}{2}\frac{S^2}{Y}$

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 $\left(B\right)$