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
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
- [JEE MAIN 2020]
- A
$\left[\frac{m_{1}+m_{2}}{\left(m_{1}+m_{2}\right) R^{2}+I}\right]^{\frac{1}{2}} g h$
- B
$\left[\frac{2\left(\mathrm{m}_{1}-\mathrm{m}_{2}\right) \mathrm{gh}}{\left(\mathrm{m}_{1}+\mathrm{m}_{2}\right) \mathrm{R}^{2}+\mathrm{I}}\right]^{\frac{1}{2}}$
- C
$\left[\frac{2\left(\mathrm{m}_{1}+\mathrm{m}_{2}\right) \mathrm{gh}}{\left(\mathrm{m}_{1}+\mathrm{m}_{2}\right) \mathrm{R}^{2}+\mathrm{I}}\right]^{\frac{1}{2}}$
- D
$\left[\frac{\left(\mathrm{m}_{1}-\mathrm{m}_{2}\right)}{\left(\mathrm{m}_{1}+\mathrm{m}_{2}\right) \mathrm{R}^{2}+\mathrm{I}}\right]^{\frac{1}{2}} \mathrm{gh}$
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