The ratio of the radius of gyration of a soli | vedclass

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(B) The radius of gyration $K$ is given by the formula $K = \sqrt{\frac{I}{M}}$,where $I$ is the moment of inertia and $M$ is the mass.For a solid sph

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$\sqrt{3}: \sqrt{5}$

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(B) The radius of gyration $K$ is given by the formula $K = \sqrt{\frac{I}{M}}$,where $I$ is the moment of inertia and $M$ is the mass.For a solid sphere,the moment of inertia about its own axis is $I_{	ext{solid}} = \frac{2}{5}MR^2$. Thus,$K_{	ext{solid}} = \sqrt{\frac{2/5 MR^2}{M}} = R\sqrt{\frac{2}{5}}$.For a thin hollow sphere,the moment of inertia about its own axis is $I_{	ext{hollow}} = \frac{2}{3}MR^2$. Thus,$K_{	ext{hollow}} = \sqrt{\frac{2/3 MR^2}{M}} = R\sqrt{\frac{2}{3}}$.The ratio is $\frac{K_{	ext{solid}}}{K_{	ext{hollow}}} = \frac{R\sqrt{2/5}}{R\sqrt{2/3}} = \sqrt{\frac{2}{5} 	imes \frac{3}{2}} = \sqrt{\frac{3}{5}} = \sqrt{3} : \sqrt{5}$.

The ratio of the radius of gyration of a solid sphere of mass $M$ and radius $R$ about its own axis to the radius of gyration of a thin hollow sphere of the same mass and radius about its axis is:

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