MHT CET202522 Apr 2025Morning ShiftPhysicsRotational MotionActual
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? [ I _ h = moment of inertia of hollow sphere about an axis coinciding with its diameter, I _ s = moment of inertia of solid sphere about an axis coinciding with its diameter]
Options
- AI _ s > I _ h
- BI _ h I _ s
- CI _ h > I _ s
- DI _ h = I _ s
Correct answer
C. I _ h > I _ s
Step-by-step 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 = 2 5 MR^2 . For a thin-walled hollow sphere of equal mass and radius, the moment of inertia is I_h = 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: 2 3 > 2 5 , so I_h > I_s . The hollow