A) \[\frac{a}{4}\]
B) \[\frac{a}{3}\]
C) \[\frac{a}{2}\]
D) \[\frac{2a}{3}\]
Correct Answer: C
Solution :
Maximum potential energy of particle executing SHM \[{{U}_{\max }}=\frac{1}{2}m{{\omega }^{2}}{{a}^{2}}\] Potential energy \[U=\frac{1}{4}{{U}_{\max }}\] (given) \[\frac{1}{2}m{{\omega }^{2}}{{y}^{2}}=\frac{1}{4}\left( \frac{1}{2}m{{\omega }^{2}}{{a}^{2}} \right)\] \[{{y}^{2}}=\frac{{{a}^{2}}}{4}\] \[\Rightarrow \]\[y=\frac{a}{2}\]
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