MHT CET202615 April 2026Morning ShiftPhysicsRotational MotionActual
If the earth suddenly contracts to ( 1 3 )^ rd of its present size without change in its mass, the ratio kinetic energy of the earth after and before contraction will be (Earth is assumed to be a rotating sphere about itself)
Options
- A9
- B5
- C7
- D6
Correct answer
A. 9
Step-by-step solution
By conservation of angular momentum, L₁ = L₂ . The rotational kinetic energy is given by K = L^2 2I . The ratio of final to initial kinetic energy is K₂ K₁ = I₁ I₂ . The moment of inertia of a solid sphere is I = 2 5 MR^2 . Given R₂ = R₁ 3 , we have I₂ = 2 5 M ( R₁ 3 )^2 = I₁ 9 . Therefore, K₂ K₁ = I₁ I₁ 9 = 9 . Answer: 9