For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is x/5. The value of x is ___________.

Solution

Physics sir · 3 steps

Rolling means v = ω R, so write both energies in terms of v and the ratio falls out.

1. Moment of inertia. A thin spherical shell has all its mass at radius R, so I = 2/3MR². For rolling without slipping, ω = v/R.
2. Two energies. Rotational: 1/2Iω² = 1/2 × 2/3MR² × v²/R² = 1/3Mv². Translational: 1/2Mv². Total: 1/3Mv² + 1/2Mv² = 5/6Mv².

   Kᵣₒₜ/Kₜₒₜₐₗ = (1/3Mv²)/(5/6Mv²) = 2/5

3. So. The ratio is 2/5, so x = 2.

The idea to keep. For any rolling body with I = kMR², the rotational share of the total KE is k/(1+k). Just know k: 2/3 for a shell, 2/5 for a solid sphere.

Answer from the NTA final answer key. Solution by PrepWiser.