A) \[\sqrt{3}:\sqrt{5}\]
B) \[\sqrt{4g}\]
C) 25 9
D) 9 25
Correct Answer: A
Solution :
Moment of inertia of a solid sphere of radius r, and mass m is \[I=\frac{2}{5}m{{r}^{2}}\], and hollow sphere \[I=\frac{2}{3}m{{r}^{2}}\] Given, \[{{I}_{solid}}={{I}_{hollow}}\] \[\therefore \] \[\frac{2}{5}\,mr_{1}^{2}=\frac{2}{3}mr_{2}^{2}\] \[\Rightarrow \] \[\frac{r_{1}^{2}}{r_{2}^{2}}=\frac{5}{3}\] \[\Rightarrow \] \[\frac{{{r}_{1}}}{{{r}_{2}}}=\frac{\sqrt{5}}{\sqrt{3}}\] \[\therefore \] \[\frac{{{r}_{2}}}{{{r}_{1}}}=\frac{\sqrt{3}}{\sqrt{5}}\]
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