A) \[\frac{a}{\sqrt{2}}\]
B) \[\frac{a}{2}\]
C) \[\frac{a}{4}\]
D) \[a\]
Correct Answer: A
Solution :
[a] If displacement of particle is y, then \[KE=\frac{1}{2}m{{\omega }^{2}}({{a}^{2}}-{{y}^{2}})\And P.E.=\frac{1}{2}m{{\omega }^{2}}{{y}^{2}}\] If \[KE=PE\] then\[\frac{1}{2}m{{\omega }^{2}}{{y}^{2}}\] \[=\frac{1}{2}m{{\omega }^{2}}{{a}^{2}}-\frac{1}{2}m{{\omega }^{2}}{{y}^{2}}\] \[\Rightarrow 2{{y}^{2}}={{a}^{2}}\,\,\,\,\,\therefore y=\frac{a}{\sqrt{2}}\]
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