Two springs of force constant 1000 N/m & 2000 N/m are stretched by same force. The ratio of their respective potential energies is

$$\begin{gathered} potential energy PE = \frac{1}{2}K{X}^2 ; K=force cons\tan t; x = displacement \\ restoring force =F =-KX \\ \Rightarrow \frac{F}{K}=-X ; substitute X value in PE equation, \\ PE =\frac{1}{2}K\frac{F^2}{K^2} =\frac{1}{2}\frac{F^2}{K} \\ for two springs, \\ P{E}_{1 }=\frac{1}{2}\frac{F^2}{K_1} \\ P{E}_{2 }=\frac{1}{2}\frac{F^2}{K_2} \\ divide the above two equations, one by the other \\ \frac{P{E}_{1 }}{P{E}_2}=\frac{K_2}{K_1} ; substitute the given vales of K_1,K_2 \\ \frac{P{E}_{1 }}{P{E}_2}==\frac{2000}{1000}=\frac{2}{1} \end{gathered}$$