A spherical shell has a mass one-fourth that | vedclass

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(B) Let the mass of the solid sphere be $M$ and its radius be $R_S$.Let the mass of the spherical shell be $M_H = \frac{M}{4}$ and its radius be $R_H$

Vedclass · Accepted Answer

$\sqrt{12} : \sqrt{5}$

Vedclass · Answer

(B) Let the mass of the solid sphere be $M$ and its radius be $R_S$.Let the mass of the spherical shell be $M_H = \frac{M}{4}$ and its radius be $R_H$.The moment of inertia of a solid sphere about its diameter is $I_{SS} = \frac{2}{5} M R_S^2$.The moment of inertia of a spherical shell about its diameter is $I_{HS} = \frac{2}{3} M_H R_H^2 = \frac{2}{3} (\frac{M}{4}) R_H^2 = \frac{1}{6} M R_H^2$.Given that $I_{HS} = I_{SS}$,we have:$\frac{1}{6} M R_H^2 = \frac{2}{5} M R_S^2$$\frac{R_H^2}{R_S^2} = \frac{2}{5} 	imes 6 = \frac{12}{5}$$\frac{R_H}{R_S} = \sqrt{\frac{12}{5}} = \frac{\sqrt{12}}{\sqrt{5}}$Thus,the ratio of their radii $R_H : R_S$ is $\sqrt{12} : \sqrt{5}$.

$A$ spherical shell has a mass one-fourth that of a solid sphere,and both have the same moment of inertia $(M.I.)$ about their respective diameters. The ratio of their radii will be:

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