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  4. For a sphere made out of a certain material, the moment of inertia of the sphere is proportional to [radius of the sphere = R ]

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Q. For a sphere made out of a certain material, the moment of inertia of the sphere is proportional to [radius of the sphere = $R$ ]

NTA AbhyasNTA Abhyas 2020System of Particles and Rotational Motion

Solution:

Moment of inertia of a solid sphere is $\frac{2}{5}mR^{2}$
$I=\frac{2}{5}mR^{2}$
$I=\frac{2}{5}V\rho R^{2}$
$I=\frac{2}{5}\times \frac{4}{3}\pi R^{3}\rho R^{2}$
$I=\frac{8}{15}\pi \rho R^{5}$
$I \propto R^{5}$