Question

if P longitudinal strain is produced in a wire of Young's modulus Q then energy stored in the material of the wire per unit volume is ​

Answer 1

Answer:

$\frac{Yp^2}{2}$

Explanation:

Given longitudinal strain = p

The Young's modulus is Y

We know that

$\boxed{Y=\frac{\text{Stress}}{\text{Strain}}}$

Therefore,

$Y=\frac{\text{Stress}}{p}$

$\implies \text{Stress}=Y\times p$

The energy stored per unit volume is given by

$E=\frac{1}{2}\times \text{Stress}\times\text{Strain}$

$E=\frac{1}{2}\times Yp\times p$

$\implies E=\frac{1}{2}Yp^2$

or, $E=\frac{Yp^2}{2}$

Hope this helps.