JEE Main · 2023 · 15 Apr 2023 · Shift 1 · Rotational Mechanics

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A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyrations respectively (

k_{sph} : k_{cyl}

) is

2 : x

, then value of

x

is ______.

Answer: 5

Solution

For a solid sphere

I = \frac{2}{5} m R^{2} = m k_{s p h}^{2}

, so

k_{s p h} = \frac{2}{5} R

. For a solid cylinder

I = \frac{1}{2} m R^{2} = m k_{cy l}^{2}

, so

k_{cy l} = \frac{R}{2}

. The ratio is

\frac{k _{s p h}}{k _{cy l}} = \frac{2/5}{1/ 2} = \frac{2}{5}

. Comparing with

\frac{2}{x}

gives

x = 5

JEE Main · 2023 · 15 Apr 2023 · Shift 1 · Integer answer

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