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)

A hollow sphere about any of its diameter

Answer 2

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.