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Two springs of spring constants $1000 N m^{- 1}$ and $2000 N m^{- 1}$ are stretched with same force. They will have potential energy in the ratio of

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$2^{2} : 1^{2}$

$1^{2} : 2^{2}$

$2 : 1$

$1 : 2$

answer is A.

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Detailed Solution

$U = \frac{1}{2} k x^{2} = \frac{F^{2}}{2 K}$

$\frac{U_{1}}{U_{2}} = \frac{K_{2}}{K_{1}} = \frac{2000}{1000} = \frac{2}{1}$

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