A uniformly thick wheel with moment of inertia I and radius R is free… | JEE Main 2020 (9 Jan, Shift 2)

Q47JEE Main 2020 · 9 JAN · SHIFT 2Medium

Rotational Kinematics & Dynamics

A uniformly thick wheel with moment of inertia I and radius R is free to rotate about its centre of mass (see fig). A massless string is wrapped over its rim and two blocks of masses m1 and m2 (m1 $>$ m2) are attached to the ends of the string. The system is released from rest. The angular speed of the wheel when m1 descents by a distance h is:

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Answer: (d)

$m_1$ falls $h$ , $m_2$ rises $h$ ; both move with $v = \omega R$ .
$(m_1 - m_2)gh = \frac{1}{2}(m_1 + m_2)\omega^2R^2 + \frac{1}{2}I\omega^2$
$\omega = \left[\frac{2(m_1 - m_2)gh}{(m_1 + m_2)R^2 + I}\right]^{1/2}$
So the answer is (d).

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