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