$A$ 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 $m_{1}$ descends by a distance $h$ is

• A
  $\left[\frac{m_{1}+m_{2}}{\left(m_{1}+m_{2}\right) R^{2}+I}\right]^{\frac{1}{2}} gh$
• B
  $\left[\frac{2\left(m_{1}-m_{2}\right) gh}{\left(m_{1}+m_{2}\right) R^{2}+I}\right]^{\frac{1}{2}}$
• C
  $\left[\frac{2\left(m_{1}+m_{2}\right) gh}{\left(m_{1}+m_{2}\right) R^{2}+I}\right]^{\frac{1}{2}}$
• D
  $\left[\frac{\left(m_{1}-m_{2}\right)}{\left(m_{1}+m_{2}\right) R^{2}+I}\right]^{\frac{1}{2}} gh$