A circular plate is rotating in horizontal plane, about an axis...

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

\omega

. A person sits at the centre having two dumbbells in his hands. When he stretched 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

\dfrac{E}{x}

. The value of

x

Correct answer

Step-by-step solution

The kinetic energy is given by

$E = \dfrac{1}{2}I{\omega}^{2} = \left(\dfrac{{L}^{2}}{2I}\right)$

It is given that the new moment of inertia

${I}^{'} = 3I$

Clearly, the final kinetic energy is

${E}_{f} = \dfrac{{L}^{2}}{2I '} = \dfrac{{L}^{2}}{6I} ⇒ {E}_{f} = \left(\dfrac{E}{3}\right)$

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