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JEE Main 2023 (15 Apr, Shift 1) · Rolling Motion

Rolling Motion question from JEE Main 2023 (15 Apr, Shift 1)

Q39JEE Main 2023 · 15 APR · SHIFT 1Medium

Rolling Motion

A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radii of gyration respectively $(k$ sph $: k$ cyl $)$ is $2 : \sqrt{x}$ . The value of $x$ is ____________.

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

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Answer: 5

Solid sphere: $k_{sph} = \sqrt{\frac{2}{5}}R$ ; solid cylinder: $k_{cyl} = \sqrt{\frac{1}{2}}R$ .
$\dfrac{k_{sph}}{k_{cyl}} = \sqrt{\dfrac{2/5}{1/2}} = \sqrt{\dfrac{4}{5}} = \dfrac{2}{\sqrt{5}}$
So $x = 5$ .

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