A mass of 2 kg falls from a height of 40 cm on a spring of force constant 1960 N/m. The spring is compressed by :

$$\begin{gathered} \mathrm{According} \mathrm{to} \mathrm{conservation} \mathrm{of} \mathrm{energy} \\ \mathrm{loss} \mathrm{in} \mathrm{total} \mathrm{potential} \mathrm{energy} \mathrm{is} \mathrm{equal} \mathrm{to} \mathrm{spring} \mathrm{energy} \\ \mathrm{mg}(\mathrm{h}+\mathrm{x})=\frac{1}{2}{\mathrm{kx}}^2 \\ 2\times 9.8\left(0.4+\mathrm{x}\right)=\frac{1}{2}1960{\mathrm{x}}^2 \\ 0.4+\mathrm{x}=50{\mathrm{x}}^2 \\ 500{\mathrm{x}}^2-10\mathrm{x}-4=0 \\ 500{\mathrm{x}}^2-50\mathrm{x}+40\mathrm{x}-4=0 \\ 50\mathrm{x}\left(10\mathrm{x}-1\right)+4\left(10\mathrm{x}-1\right)=0 \\ \mathrm{x}=\frac{1}{10}\mathrm{m}=10 \mathrm{cm} \end{gathered}$$