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JEE Main 2024 (27 Jan, Shift 2) · Rolling Motion

Rolling Motion question from JEE Main 2024 (27 Jan, Shift 2)

Q31JEE Main 2024 · 27 JAN · SHIFT 2Medium

Rolling Motion

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 $\frac{7}{x}$ , where $x$ is _________.

Numerical answer type. Work it out, then open the answer.

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Answer: 7

Starting from rest, each body's total KE at the bottom equals the PE lost, $mgh$ , whatever its shape.
Taking equal masses and the same height, $KE_{ring} : KE_{sphere} = 1 = \dfrac{7}{7}$ .
So $x = 7$ .

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