Question

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

• A. A ring about its axis, perpendicular to the plane of the ring.
• B. A disc about its axis, perpendicular to the plane of the ring.
• C. A solid sphere about one of its diameters
• D. A spherical shell about one of its diameters.

Answer 1

The correct option is A A ring about its axis, perpendicular to the plane of the ring.

(a) Moment of inertia of a ring about its axis and perpendicular to its plane $=M{r}^2$
(b) Moment of inertia of a disc about its axis and perpendicular to its plane $=\frac{1}{2}M{r}^2=0.5M{r}^2$
(c) Moment of inertia of a solid sphere about one of its diameter $=\frac{2}{5}M{r}^2=0.4M{r}^2$
(d) Moment of inertia of a spherical shell about one of its diameter $=\frac{2}{3}M{r}^2=0.66M{r}^2$
Therefore, the moment of inertia of the ring is highest.