A circular plate is rotating in horizontal plane, about an axis p… - Vidyadip

MCQ

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

✓
$3$
B
$6$
C
$9$
D
$12$

✓

Answer

Correct option: A.

$3$

a
$KE =\frac{ L ^2}{2 I } \Rightarrow \frac{ KE _{\text {fimpl }}}{ KE _{\text {initial }}}=\frac{ I _{\text {intitial }}}{ I _{\text {final }}} \Rightarrow \frac{ KE _{\text {fimpl }}}{ E }=\frac{1}{3}$

$\Rightarrow KE _{\text {fimel }}=\frac{E}{3}$

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