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 \(\mathrm{m}_{1}\) and \(\mathrm{m}_{2}\left(\mathrm{m}_{1}>\mathrm{m}_{2}\right)\) are attached to the ends of the string. The system is released from rest. The angular speed of the wheel when \(\mathrm{m}_{1}\) descents by a distance \(h\) is

1. A \(\left[\frac{m_{1}+m_{2}}{\left(m_{1}+m_{2}\right) R^{2}+I}\right]^{\frac{1}{2}} g h\)
2. B \(\left[\frac{2\left(\mathrm{m}_{1}-\mathrm{m}_{2}\right) \mathrm{gh}}{\left(\mathrm{m}_{1}+\mathrm{m}_{2}\right) \mathrm{R}^{2}+\mathrm{I}}\right]^{\frac{1}{2}}\)
3. C \(\left[\frac{2\left(\mathrm{m}_{1}+\mathrm{m}_{2}\right) \mathrm{gh}}{\left(\mathrm{m}_{1}+\mathrm{m}_{2}\right) \mathrm{R}^{2}+\mathrm{I}}\right]^{\frac{1}{2}}\)
4. D \(\left[\frac{\left(\mathrm{m}_{1}-\mathrm{m}_{2}\right)}{\left(\mathrm{m}_{1}+\mathrm{m}_{2}\right) \mathrm{R}^{2}+\mathrm{I}}\right]^{\frac{1}{2}} \mathrm{gh}\)