A) zero
B) \[\frac{1}{2}\]
C) \[\frac{1}{4}\]
D) \[\frac{3}{4}\]
Correct Answer: C
Solution :
Total energy, \[E=\frac{1}{2}m\,{{\omega }^{2}}{{a}^{2}}\] \[KE=\frac{1}{2}m{{\omega }^{2}}{{y}^{2}}\] According to question, \[y=\frac{a}{2}\] \[KE=\frac{1}{2}m{{\omega }^{2}}{{\left( \frac{a}{2} \right)}^{2}}\] \[=\frac{1}{2}m{{\omega }^{2}}\frac{{{a}^{2}}}{4}\] \[=\frac{1}{4}\left( \frac{1}{2}m{{\omega }^{2}}{{a}^{2}} \right)\] \[=\frac{1}{4}E\] Therefore, KE is\[\frac{1}{4}\]times of total energy.
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