A) 3/5
B) 2/7
C) 2/5
D) 3/7
Correct Answer: B
Solution :
Rotational energy of sphere \[{{E}_{R}}=\frac{1}{2}I{{\omega }^{2}}\] For sphere, moment of inertia \[I=\frac{2}{5}m{{R}^{2}}\] \[\therefore \] \[{{E}_{R}}=\frac{1}{2}\left( \frac{2}{5}m{{R}^{2}} \right){{\left( \frac{v}{R} \right)}^{2}}\] \[=\frac{1}{5}m{{v}^{2}}\] Translational kinetic energy\[{{E}_{r}}=\frac{1}{2}m{{v}^{2}}\] \[\therefore \] Total energy\[=\frac{1}{5}m{{v}^{2}}+\frac{1}{2}m{{v}^{2}}\] \[=\frac{7}{10}m{{v}^{2}}\] \[\therefore \] Required fraction \[=\frac{\frac{1}{5}m{{v}^{2}}}{\frac{7}{10}m{{v}^{2}}}\] \[=\frac{2}{7}\]
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