$\begin{array}{1 1}(A)\;1 : 1\\(B)\;2 : 1\\(C)\;1 : 2\\(D)\;1 : 4\end{array} $

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Work of gravitional force is $=mgx_0$

Where $x_0$ is extension.

Let f be the spring force

$Y=(\large\frac{f}{a})\times \frac{l}{x}$

$f=\large\frac{Yax}{l}$

$Work_{spring}=\int\limits_0^{x_0} fdx$

$\quad\;\;\;=\large\frac{1}{2}\frac{Yax_0^2}{l}$

As $mg=\large\frac{Yax_0}{l}$

$Work_{spring}=\large\frac{mg x_0}{2}$

So $\large\frac{Work_{gravity}}{Work_{spring}}=\frac{mgx_0}{mgx_0/2}$

$\Rightarrow \large\frac{2}{1}$

Hence (B) is the correct answer.

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