A) \[5\sqrt{2}\,cm\]
B) \[10\sqrt{2}\,cm\]
C) \[3\sqrt{2}\,cm\]
D) \[10\,cm\]
Correct Answer: A
Solution :
Given, A = 10 cm Let the position of particle is x cm According to question, KE = PE \[\Rightarrow \] \[\frac{1}{2}m\,{{\omega }^{2}}({{A}^{2}}-{{x}^{2}})=\frac{1}{2}m\,{{\omega }^{2}}{{x}^{2}}\] \[\Rightarrow \] \[{{A}^{2}}-{{x}^{2}}={{x}^{2}}\] \[\Rightarrow \] \[{{A}^{2}}=2{{x}^{2}}\] \[\Rightarrow \] \[2{{x}^{2}}={{10}^{2}}\] \[\Rightarrow \] \[{{x}^{2}}=\frac{100}{2}=60\] \[\Rightarrow \] \[x=5\sqrt{2}\,cm.\]
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