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

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Solution

The correct option is C
When the springs are stretched by the same force F, the extensions in springs A and B are and respectively which are given by
$F = k_{1} x_{1} = k_{2} x_{2} o r \frac{x_{1}}{x_{2}} = \frac{k_{2}}{k_{1}} (i)$
Work done $w_{1} = \frac{1}{2} k_{1} x_{1}^{2} a n d w_{2} = \frac{1}{2} k_{2} x_{2}^{2}$
$∴ \frac{w_{1}}{w_{2}} = \frac{k_{1}}{k_{2}} . \frac{x_{1}^{2}}{x_{2}^{2}}$ (ii)
Using (i) and (ii) we get $\frac{w_{1}}{w_{2}} = \frac{k_{1}}{k_{2}} . \frac{k_{2}^{2}}{k_{1}^{2}}$
Hence the correct choice is (c)

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Two springs A and B have force constants k1 andk2 respectively. The ratio of the work done on A to that done on B when they are stretched by the same force is

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