AP EAMCET20224 Jul 2022Evening ShiftPhysicsRotational MotionActual
A solid sphere of radius R has its outer half removed, so that its radius becomes R 2 . Then its moment of inertia about the diameter is
Options
- Abecomes 1 2 of its intial volume
- Bis unchanged
- Cbecomes 1 16 of initial volume.
- Dbecomes 1 32 of initial volume.
Correct answer
D. becomes 1 32 of initial volume.
Step-by-step solution
Moment of inertia of a solid sphere is given by, I = 2 5 M R 2 = 2 5 ρ 4 3 π R 3 R 2 = 8 15 ρ π R 5 . Therefore, for constant density, the moment of inertia I ∝ R 5 . ⇒ I 1 I 2 = R 1 R 2 5 ⇒ I 2 = 1 2 5 I 1 ⇒ I 2 = 1 32 I 1