Question 43 - 2020 (09 Jan Shift 2)

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 $m_1$ and $m_2$ ($m_1 > m_2$) are attached to the ends of the string. The system is released from rest. The angular speed of the wheel when $m_1$ descents by a distance $h$ is:

(1) $\left[\frac{2(m_1 - m_2)gh}{(m_1 + m_2)R^2 + I}\right]^{1/2}$

(2) $\left[\frac{2(m_1 + m_2)gh}{(m_1 + m_2)R^2 + I}\right]^{1/2}$

(3) $\left[\frac{(m_1 - m_2)}{(m_1 + m_2)R^2 + I}\right]^{1/2}gh$

(4) $\left[\frac{m_1 + m_2}{(m_1 + m_2)R^2 + I}\right]^{1/2}gh$