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. $I _ { \text {ring } } = \frac { 1 } { 2 } M R ^ { 2 }$

Moment of inertia of a disc about any of its diameter is

Moment of inertia of a hollow sphere about any of its diameter is.

$I _ { \text {hollowsphere } } = \frac { 2 } { 3 } M R ^ { 2 }$

Moment of inertia of a solid sphere about any of its diameter is.

$I _ { \text {solidsphere } } = \frac { 2 } { 5 } M R ^ { 2 }$

Thus, is largest.