A) \[{{\left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)}^{2}}\]
B) \[{{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}\]
C) \[\frac{{{r}_{1}}}{{{r}_{2}}}\]
D) \[\frac{{{r}_{2}}}{{{r}_{1}}}\]
Correct Answer: B
Solution :
Kinetic energy (K) of rotation is \[K=\frac{1}{2}I{{\omega }^{2}}\] where \[\omega =\frac{v}{r},r\]is radius of circle. \[\therefore \] \[K=\frac{1}{2}I\left( \frac{{{v}^{2}}}{{{r}^{2}}} \right)\] \[\therefore \] \[\frac{{{K}_{1}}}{{{K}_{2}}}=\frac{r_{2}^{2}}{r_{1}^{2}}\] \[\Rightarrow \] \[\frac{{{K}_{2}}}{{{K}_{1}}}\frac{r_{1}^{2}}{r_{2}^{2}}\]
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