Two springs A and B have force constants $k_{1}$ and $k_{2}$ respectively. The ratio of work done on A to that done on B when they are stretched by the same force is

$\frac{k_{1}}{k_{2}}$

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$\sqrt{\frac{k_{1}}{k_{2}}}$

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$\frac{k_{2}}{k_{1}}$

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$\sqrt{\frac{k_{2}}{k_{1}}}$

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Solution

The correct option is C
$\frac{k_{2}}{k_{1}}$

When the springs are stretched by the same force $F$ , let the extensions be $x_{1}$ and $x_{2}$ .
So, $F = k_{1} x_{1} = k_{2} x_{2} \Rightarrow \frac{x_{1}}{x_{2}} = \frac{k_{2}}{k_{1}}$
Now, ratio of work done, $\frac{W_{1}}{W_{2}} = \frac{\frac{1}{2} k_{1} x_{1}^{2}}{\frac{1}{2} k_{2} x_{2}^{2}} = \frac{k_{1} x_{1} \times x_{1}}{k_{2} x_{2} \times x_{2}} = \frac{x_{1}}{x_{2}} = \frac{k_{2}}{k_{1}}$
Hence, the correct choice is (c).

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