A) 10 U
B) 25 U
C) U/5
D) 5 U
Correct Answer: B
Solution :
Potential energy in a stretched spring is given by \[U=\frac{1}{2}k\,{{x}^{2}}\] \[\therefore \frac{{{U}_{1}}}{{{U}_{2}}}={{\left( \frac{{{x}_{1}}}{{{x}_{2}}} \right)}^{2}}\] Given, \[{{x}_{1}}=2\,cm\,=0.02\,m,\,\,{{x}_{2}}=10\,cm=0.1\,m\] Substituting the values, we have \[\frac{{{U}_{1}}}{{{U}_{2}}}={{\left( \frac{0.02}{0.1} \right)}^{2}}={{\left( \frac{1}{5} \right)}^{2}}=\frac{1}{25}\] \[\Rightarrow {{U}_{2}}=25\,{{U}_{1}}=25\,U\]
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