A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies is where is ____.
Answer: 7
Solution
In pure rolling without slipping, static friction acts at the point of the body in contact with the incline, which is instantaneously at rest, so it does no work. Mechanical energy is therefore conserved for both bodies. Starting from rest at the same height on the same incline, the ring and the sphere convert identical potential energy into kinetic energy, regardless of how that energy splits between translation and rotation — the split depends on the moment of inertia, but the total does not. So the ratio of their final kinetic energies is 1, giving .
JEE Main · 2024 · 27 Jan 2024 · Shift 2 · Integer answer