A circular rotating |SomeBasicConceptsofChemistryJEEMain2023

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JEE MAIN 2023

11-4-2023

Question

A circular plate is rotating in horizontal plane, about an axis passing through its center and perpendicular to the plate, with an angular velocity . 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 . The value of x is-

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Solution

Sol. $$ \begin{aligned} & K E=\frac{L^2}{2} \Rightarrow \frac{K E_{\text {final }}}{K E_{\text {initial }}}=\frac{I_{\text {initial }}}{I_{\text {final }}} \Rightarrow \frac{K E_{\text {final }}}{E}=\frac{1}{3} \\ & \Rightarrow K E_{\text {final }}=\frac{E}{3} \end{aligned} $$

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