A) 4\[U\]
B) 8\[U\]
C) 16\[U\]
D) \[U\]/4
Correct Answer: C
Solution :
Let extension produced in a spring be x initially. In stretched condition spring will have potential energy \[U=\frac{1}{2}k{{x}^{2}}\] Where k is spring constant or force constant, \[\therefore \] \[\frac{{{U}_{1}}}{{{U}_{2}}}=\frac{x_{1}^{2}}{x_{2}^{2}}\] ??..(i) Given, \[{{U}_{1}}=U,\,{{x}_{1}}=2cm,\,\,{{x}_{2}}=8cm\] Putting these values in Eq. (i), we have \[\frac{U}{{{U}_{2}}}=\frac{{{(2)}^{2}}}{{{(8)}^{2}}}\] \[=\frac{4}{64}=\frac{1}{16}\] \[\therefore \] \[{{U}_{2}}=16U\]
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