A) \[\frac{1}{6}s\]
B) \[\frac{1}{4}s\]
C) \[\frac{1}{3}s\]
D) \[\frac{1}{12}s\]
Correct Answer: A
Solution :
[a] \[K.E.=\frac{1}{2}m{{a}^{2}}{{\omega }^{2}}{{\cos }^{2}}\omega t\] and \[T.E.=\frac{1}{2}m{{a}^{2}}{{\omega }^{2}}\] Given \[K.E.=0.75T.E.\] \[\Rightarrow \,0.75={{\cos }^{2}}\omega t\Rightarrow \omega t=\frac{\pi }{6}\] \[\Rightarrow \,t=\frac{\pi }{6\times \omega }\Rightarrow t=\frac{\pi \times 2}{6\times 2\pi }\Rightarrow t=\frac{1}{6}s\]
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