A) \[\frac{a}{2}\]
B) \[\frac{a}{\sqrt{2}}\]
C) \[\sqrt{2a}\]
D) \[\frac{a}{3}\]
Correct Answer: B
Solution :
The kinetic energy (KE) of a body executing SHM with amplitude a undergoing displace- ment y is \[KE=\frac{1}{2}m{{\omega }^{2}}({{a}^{2}}-{{y}^{2}})\] ...(i) where\[\omega \]is angular velocity, and m the mass. Also, potential energy (PE) is \[PE=\frac{1}{2}m{{\omega }^{2}}{{y}^{2}}\] ...(ii) Given, \[KE=PE\] \[\therefore \] \[\frac{1}{2}m{{\omega }^{2}}({{a}^{2}}-{{y}^{2}})=\frac{1}{2}m{{\omega }^{2}}{{y}^{2}}\] \[\Rightarrow \] \[{{a}^{2}}-{{y}^{2}}={{y}^{2}}\] \[\Rightarrow \] \[y=\frac{a}{\sqrt{2}}\]
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