A) \[\frac{1}{16}\]
B) \[\frac{1}{8}\]
C) \[\frac{1}{2}\]
D) \[\frac{1}{4}\]
Correct Answer: D
Solution :
[d]: In SHM. Potential energy of a particle,\[U=\frac{1}{2}m{{\omega }^{2}}{{x}^{2}}\] Total energy of a particle,\[E=\frac{1}{2}m{{\omega }^{2}}{{A}^{2}}\]where symbols have their usual meaning At \[x=\frac{A}{2},\]the fraction of total energy which is potential,\[\frac{U}{E}=\frac{\frac{1}{2}m{{\omega }^{2}}{{x}^{2}}}{\frac{1}{2}m{{\omega }^{2}}{{A}^{2}}}=\frac{{{x}^{2}}}{{{A}^{2}}}={{\left[ \frac{A/2}{A} \right]}^{2}}=\frac{1}{4}\]
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