Question

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

• A. A ring about any of its diameter
• B. A disc about any of its diameter
• C. A hollow sphere about any of its diameter
• D. A solid sphere about any of its diameter

Answer 1

Answer: (C)

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