The potential energy of a long spring when stretched by 2 ~cm is U...

Potential energy of a spring \begin{aligned} & \begin{aligned} &= \frac{1}{2} \times \text{ force constant } \\ & \times(\text{ extension })^2 \\ & \Rightarrow \text{ Potential energy } \propto(\text{ extension })^2 \end{aligned} \\ & \text{Hence } \frac{U_1}{V_2}=\left(\frac{x_1}{x_2}\right)^2 \\ & \Rightarrow \frac{V_1}{V_2}=\left(\frac{2}{8}\right)^2 \\ & \Rightarrow \frac{U_1}{U_2}- \frac{1}{16}\left(\because U_1=V\right) \end{aligned}$