Question

A wire of length $L$ and cross-sectional A is made of a material of Young's modulus. If the wire is stretched by an amount x, the work done is....................

Answer 1

Work done is equal to the potential energy stored in the wire.

$\therefore$ $W=U=\frac{1}{2}\times Stress\times Strain\times Volume$

OR $W=\frac{1}{2}\times Y(Strain{)}^2\times Volume$ .............(1) $(Strain=Y\times Strain)$

$Strain=\frac{x}{L}$ and Volume$=AL$

$\therefore$ $W=\frac{1}{2}\times Y\times \frac{x^2}{L^2}\times AL$ $⟹W=\frac{Y{x}^{2}A}{2L}$