question_answer

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 warapped 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 [JEE MAIN Held on 09-01-2020 Evening]

A) \[{{\left[ \frac{({{m}_{1}}-{{m}_{2}})}{({{m}_{1}}+{{m}_{2}}){{R}^{2}}+I} \right]}^{\frac{1}{2}}}gh\]

B) \[{{\left[ \frac{2({{m}_{1}}-{{m}_{2}})gh}{({{m}_{1}}+{{m}_{2}}){{R}^{2}}+I} \right]}^{\frac{1}{2}}}\]

C) \[{{\left[ \frac{{{m}_{1}}+{{m}_{2}}}{({{m}_{1}}+{{m}_{2}}){{R}^{2}}+I} \right]}^{\frac{1}{2}}}gh\]

D) \[{{\left[ \frac{2({{m}_{1}}+{{m}_{2}})gh}{({{m}_{1}}+{{m}_{2}}){{R}^{2}}+I} \right]}^{\frac{1}{2}}}\]