A) \[\frac{5}{7}\]rotational and \[\frac{2}{7}\]translational
B) \[\frac{2}{7}\]rotational and \[\frac{5}{7}\]translational
C) \[\frac{2}{5}\]rotational and \[\frac{3}{5}\]translational
D) \[\frac{1}{2}\]rotational and \[\frac{1}{2}\]translational
Correct Answer: B
Solution :
\[K.{{E}_{rotational}}=\frac{1}{2}I{{\omega }^{2}}\] \[=\frac{1}{2}\frac{2}{5}\omega {{r}^{2}}{{d}^{2}}\left( \because {{I}_{Solid\,sphere}}=\frac{2}{5}m{{r}^{2}} \right)\] \[K.{{E}_{translational}}=\frac{1}{2}m{{v}^{2}}\] \[\therefore \]\[\frac{K.{{E}_{rotational}}}{K.{{E}_{translational}}}=\frac{2}{5}\] Hence option (b) is correct
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