Q 11-06-088JEE MainJEE Main 2024 (27 Jan, Shift 2)Medium
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 $\dfrac{7}{x}$, where $x$ is ______.
Numerical value type. Enter your answer.
Answer: 7
In rolling without slipping, static friction does no work, so mechanical energy is conserved. Taking bodies of equal mass that descend the same height $h$, each gains kinetic energy (translational + rotational) equal to the loss in potential energy:
$$K_{ring} = K_{sphere} = mgh$$
Only the split between translational and rotational energy differs. The ratio is $1 = \dfrac77$, so $x = 7$.
Solution by Sreeraj P, M.Sc Physics