A) \[5:7\]
B) \[3:5\]
C) \[\sqrt{3}:\sqrt{5}\]
D) \[\sqrt{3}:\sqrt{7}\]
Correct Answer: C
Solution :
Let the radii of the thin spherical and the solid sphere are\[{{R}_{1}}\]and\[{{R}_{2}}\]respectively. Then the moment of inertia of the spherical shell about their diameter \[I=\frac{2}{3}MR_{1}^{2}\] ... (i) and the moment of inertia of the solid sphere is given by \[I=\frac{2}{5}MR_{2}^{2}\] ... (ii) Given that the masses and moment of inertia for both the bodies are equal, then from. Eqs. (i) and (ii) \[\frac{2}{3}MR_{1}^{2}=\frac{2}{5}MR_{2}^{2}\Rightarrow \frac{R_{1}^{2}}{R_{2}^{2}}=\frac{3}{5}\] \[\Rightarrow \] \[\frac{R}{{{R}_{2}}}=\sqrt{\frac{3}{5}}\Rightarrow {{R}_{1}}:{{R}_{2}}=\sqrt{3}:\sqrt{5}\]
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