As shown in the figure, a bob of mass m is tied by a massless string… | JEE Main 2020 (7 Jan, Shift 1)

Q48JEE Main 2020 · 7 JAN · SHIFT 1Medium

Rotational Kinematics & Dynamics

As shown in the figure, a bob of mass m is tied by a massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass m. When released from rest the bob starts falling vertically. When it has covered a distance of h, the angular speed of the wheel will be:

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Answer: (c)

Energy: $mgh = \frac{1}{2}mv^2 + \frac{1}{2}\left(\frac{1}{2}mr^2\right)\omega^2$ with $v = \omega r$ .
$mgh = \frac{3}{4}m\omega^2r^2 \Rightarrow \omega^2 = \frac{4gh}{3r^2}$
So the answer is (c) $\frac{1}{r}\sqrt{\frac{4gh}{3}}$ .

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