Physics - W.E.P. Question with Solution | TestHub

In the string elastic force is conservative in nature. $\therefore \mathrm{W}=-\Delta \mathrm{U}$ Work done by elastic force of string, $$\begin{array}{rl}\mathrm{W}& =-\left({\mathrm{U}}_{\mathrm{F}}-{\mathrm{U}}_{\mathrm{i}}\right)={\mathrm{U}}_{\mathrm{i}}-{\mathrm{U}}_{\mathrm{F}}\\ \mathrm{W}& =\frac{1}{2}\mathrm{k}{\mathrm{x}}^2-\frac{\mathrm{k}}{2}(\mathrm{x}+\mathrm{y}{)}^2\\ & =\frac{1}{2}\mathrm{k}{\mathrm{x}}^2-\frac{1}{2}\mathrm{k}\left({\mathrm{x}}^2+{\mathrm{y}}^2+2\mathrm{xy}\right)\\ & =\frac{1}{2}\mathrm{k}{\mathrm{x}}^2-\frac{1}{2}\mathrm{k}{\mathrm{y}}^2-\frac{1}{2}{\mathrm{kx}}^2-\frac{1}{2}\mathrm{k}(2\mathrm{xy})\\ & =-\mathrm{kxy}-\frac{1}{2}\mathrm{k}{\mathrm{y}}^2\end{array}$$ Therefore, the work done against elastic force ${\mathrm{W}}_{\text{external }}=-\mathrm{W}=\frac{\mathrm{K}y}{2}(2\mathrm{x}+\mathrm{y})$