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# When the load is hang from a string then the ratio of work done by gravity to the work done spring force is

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

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.