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  4. The moment of inertia and mass of hollow sphere and solid sphere is equal then what is ratio between their radius?

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Q. The moment of inertia and mass of hollow sphere and solid sphere is equal then what is ratio between their radius?

Rajasthan PMTRajasthan PMT 1998

Solution:

For solid sphere, moment of inertia $ {{I}_{1}}=\frac{2}{5}M{{R}_{1}}^{2} $ For hollow sphere $ {{I}_{2}}=\frac{2}{3}M{{R}_{2}}^{2} $ Taking, $ {{I}_{1}}={{I}_{2}} $ $ \frac{{{R}_{1}}}{{{R}_{2}}}=\sqrt{\frac{5}{3}}=\sqrt{5}:\sqrt{3} $