Q111 / 150 · MHT CET 2025 (22 Apr Shift 1) · Physics
A solid sphere and thin walled hollow sphere have same mass and same material. Which of them have greater moment of inertia about their diameter?
[ $\mathrm{I}_{\mathrm{h}}=$ moment of inertia of hollow sphere about an axis coinciding with its diameter, $\mathrm{I}_{\mathrm{s}}=$ moment of inertia of solid sphere about an axis coinciding with its diameter]
- A$\mathrm{I}_{\mathrm{s}}>\mathrm{I}_{\mathrm{h}}$
- B$\mathrm{I}_{\mathrm{h}} \geqslant \mathrm{I}_{\mathrm{s}}$
- Correct answerC$\mathrm{I}_{\mathrm{h}}>\mathrm{I}_{\mathrm{s}}$
- D$\mathrm{I}_{\mathrm{h}}=\mathrm{I}_{\mathrm{s}}$
Solution
The moment of inertia depends on both the mass and its distribution relative to the rotation axis. For a solid sphere of mass $M$ and radius $R$, the moment of inertia about a diameter is $I_s = \frac{2}{5}MR^2$.
For a thin-walled hollow sphere of equal mass and radius, the moment of inertia is $I_h = \frac{2}{3}MR^2$.
Since the mass in the hollow sphere is concentrated entirely at its outer surface, it is distributed farther from the axis of rotation. The coefficients confirm this relationship: $\frac{2}{3} > \frac{2}{5}$, so $I_h > I_s$.
The hollow sphere has greater moment of inertia.
Hence, the correct answer is option: 'C'.