A) \[\frac{a}{\sqrt{2}}\]
B) \[\frac{a}{2}\]
C) \[\frac{a}{\sqrt{\left( \frac{3}{2} \right)}}\]
D) \[\frac{a}{\sqrt{3}}\]
Correct Answer: B
Solution :
\[K=\frac{1}{2}m{{\omega }^{2}}({{a}^{2}}-{{y}^{2}})\] \[\frac{3}{4}E=\frac{1}{2}m{{\omega }^{2}}({{a}^{2}}-{{y}^{2}})\] \[\frac{3}{4}\left( \frac{1}{2}m{{\omega }^{2}}{{a}^{2}} \right)=\frac{1}{2}m{{\omega }^{2}}({{a}^{2}}-{{y}^{2}})\] \[{{y}^{2}}={{a}^{2}}-\frac{3}{4}{{a}^{2}}=\frac{{{a}^{2}}}{4}\] \[\Rightarrow \] \[y=\frac{a}{2}\]
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