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, \[{{U}_{1}}=U,{{x}_{1}}=2\,cm,\,{{x}_{2}}=8\,cm\] Putting these values in Eq. (i), we have \[\frac{U}{{{U}_{2}}}=\frac{{{(2)}^{2}}}{{{(8)}^{2}}}=\frac{4}{64}=\frac{1}{16}\] \[\therefore \]\[{{U}_{2}}=16\,U\]
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