A) 2/3
B) 2/5
C) 2/7
D) 2/9
Correct Answer: B
Solution :
The translational kinetic energy of a sphere is \[{{K}_{T}}=\frac{1}{2}m{{\upsilon }^{2}}\] and rotational kinetic energy of a sphere is \[{{K}_{R}}=\frac{1}{2}I{{\omega }^{2}}=\frac{1}{2}\times \frac{5}{2}m{{r}^{2}}\times {{\left( \frac{\upsilon }{r} \right)}^{2}}\] \[{{K}_{R}}=\frac{5}{4}m{{v}^{2}}\] \[\left( \begin{align} & \because \,v=r\omega \\ & \,\,I=\frac{5}{2}m{{r}^{2}} \\ \end{align} \right)\] Hence, \[\frac{{{K}_{T}}}{{{K}_{R}}}=\frac{\frac{1}{2}m{{\upsilon }^{2}}}{\frac{5}{4}m{{\upsilon }^{2}}}=\frac{1}{2}\times \frac{4}{5}=\frac{2}{5}\]
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