JEE Main · 2023 · 11 Apr 2023 · Shift 2 · Rotational Mechanics

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A circular plate is rotating in horizontal plane, about an axis passing through its center and perpendicular to the plate, with an angular velocity

ω

. A person sits at the center having two dumbbells in his hands. When he stretches out his hands, the moment of inertia of the system becomes triple. If E be the initial Kinetic energy of the system, then final Kinetic energy will be

\frac{E}{x}

. The value of

x

Answer: 3

Solution

By conservation of angular momentum:

L = I ω = constant

. The kinetic energy is

K E = \frac{L ^{2}}{2 I}

. Therefore,

\frac{K E _{final}}{K E _{initial}} = \frac{I _{initial}}{I _{final}}

. Given

I_{final} = 3 I_{initial}

, we have

\frac{K E _{final}}{E} = \frac{1}{3}

. Thus,

K E_{final} = \frac{E}{3}

, giving

x = 3

JEE Main · 2023 · 11 Apr 2023 · Shift 2 · Integer answer

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