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  4. Which of the following has the highest moment of inertia when each of them has the same mass and the same radius?

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Q. Which of the following has the highest moment of inertia when each of them has the same mass and the same radius?

System of Particles and Rotational Motion

Solution:

Let $M$ and $R$ be the mass and radius respectively. Moment of inertia of a ring about any of its diameter is
$I_{\text{ring}} =\frac{1}{2}MR^2$
Moment of inertia of a disc about any of its diameter is
$I_{\text{disc}} =\frac{1}{4}MR^2$
Moment of inertia of a hollow sphere about any of its diameter is
$I_{\text{hollow sphere}} =\frac{2}{3}MR^2$
Moment of inertia of a solid sphere about any of its diameter is
$I_{\text{solid sphere}} =\frac{2}{5}MR^2$
Thus, $I_{\text{hollow sphere}}$ Is largest.