A) \[\frac{U}{25}\]
B) \[\frac{U}{5}\]
C) \[3U\]
D) \[25U\]
Correct Answer: D
Solution :
When a spring is stretched by \[x\,cm,\]its stored potential energy is \[U=\frac{1}{2}k{{x}^{2}}\] where k is spring constant. Given, \[{{U}_{1}}=U,\,{{x}_{1}}=2cm,\,{{x}_{2}}=10\,cm.\] \[\therefore \] \[\frac{{{U}_{1}}}{{{U}_{2}}}=\frac{x_{1}^{2}}{x_{2}^{2}}\] \[\Rightarrow \] \[\frac{U}{{{U}_{2}}}=\frac{{{(2)}^{2}}}{{{(10)}^{2}}}\] \[\Rightarrow \] \[{{U}_{2}}=\frac{100}{4}U=25\,U\] Note: On stretching the spring further potential energy increases.
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