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Q.
The potential energy of a long spring when stretched by $2\, cm$ is $U$. If the spring is stretched by $8 \,cm$ the potential energy stored in it is
AIPMTAIPMT 2006Work, Energy and Power
Solution:
Potential energy of a spring
$=\frac{1}{2} \times \text { force constant } \times(\text { extension })^{2}$
$\therefore $ Potential energy $\propto(\text { extension })^{2}$.
or, $\frac{U_{1}}{U_{2}}=\left(\frac{x_{1}}{x_{2}}\right)^{2}$
or, $\frac{U_{1}}{U_{2}}=\left(\frac{2}{8}\right)^{2}$
or, $\frac{U_{1}}{U_{2}}=\frac{1}{16}$
or, $U_{2}=16 U_{1}=16\, U $
$ \left(\because U_{1}=U\right)$