A) \[2K\]
B) \[\sqrt{2}K\]
C) \[\frac{5}{8}K\]
D) \[\frac{5}{3}K\]
Correct Answer: C
Solution :
\[V=\omega \sqrt{({{a}^{2}}-{{X}^{2}})}\] \[V\,\propto \,\sqrt{({{A}^{2}}-{{x}^{2}})}\] At \[x=A/3\] \[\sqrt{({{A}^{2}}-{{x}^{2}})}=\sqrt{\left( {{A}^{2}}-\frac{{{A}^{2}}}{9} \right)}=A\sqrt{\frac{8}{9}}\] At \[x=2A/3\] \[\sqrt{({{A}^{2}}-{{x}^{2}})}=\sqrt{\left( {{A}^{2}}-\frac{4{{A}^{2}}}{9} \right)}=A\sqrt{\frac{5}{9}}\] \[K=1/2m\,{{v}^{2}}\] KE at\[x=2A/3=\frac{5}{9}\times \frac{9}{8}=\frac{5}{8}\,K.\]
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