The ratio of radius of gyration of a solid sphere of mass M and...

Radius of gyration of solid sphere about its own axis is given by,

${k}_{solid} = \sqrt{\dfrac{I}{M}} = \sqrt{\dfrac{\dfrac{2M{R}^{2}}{5}}{M}} = \sqrt{\dfrac{2}{5}}R$

Similarly,

${k}_{hollow} = \sqrt{\dfrac{I}{M}} = \sqrt{\dfrac{\dfrac{2M{R}^{2}}{3}}{M}} = \sqrt{\dfrac{2}{3}}R$

Therefore, required ratio would be

$\dfrac{{k}_{solid}}{{k}_{hollow}} = \sqrt{\dfrac{3}{5}}$.

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