A) \[\frac{7}{2}\]
B) \[\frac{2}{7}\]
C) \[\frac{5}{7}\]
D) \[\frac{7}{5}\]
Correct Answer: B
Solution :
\[{{(KE)}_{rotation}}=\frac{1}{2}/{{\omega }^{2}}=\frac{1}{2}\left( \frac{2}{5}M{{R}^{2}} \right){{\omega }^{2}}\] \[=\,\,\,\frac{1}{5}M{{R}^{2}}\,{{\omega }^{2}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( \because \,\,\,l=\frac{2}{5}M{{R}^{2}} \right)\] \[{{(KE)}_{translation}}=\frac{1}{2}M{{v}^{2}}=\frac{1}{2}M{{R}^{2}}\,{{\omega }^{2}}\] \[{{(KE)}_{Total}}=\,\,\frac{7}{10}M{{R}^{2}}\,{{\omega }^{2}}\] \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{{{(KE)}_{rotation}}}{{{(KE)}_{Total}}}=\frac{2}{7}\]
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