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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 m1 and m2 (m1 m2 ) are attached to the ends of the string. The system Is released from rest. The angular speed of the wheel when m1 descends by a distance h is:

[ 2 (m1-m2 )gh (m1+m2 )R^2+I ]^(1)/(2)

[ 2 (m1+m2 )gh (m1+m2 )R^2+I ]^(1)/(2)

[ (m1-m2 ) (m1+m2 )R^2+1 ]^(1)/(2)gh

[ m1+m2 (m1+m2 )R^2+I ]^(1)/(2)gh

Rotational Motion

JEE Main level, single correct, medium

170 of 280

Question 170 of 280

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 ${m}_{2}\left({m}_{1}\gt {m}_{2}\right)$ 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:

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

T{E}_{i}=T{E}_{f} {K}_{i}+{U}_{i}={K}_{linear}+{K}_{rotational}+{U}_{final}

0+0=\dfrac{1}{2}{m}_{2}{v}^{2}+\dfrac{1}{2}{m}_{1}{v}^{2}+\dfrac{1}{2}I{\omega }^{2}-{m}_{1}gh+{m}_{2}gh

\sqrt{\dfrac{2\left({m}_{1}-{m}_{2}\right)gh}{\left({m}_{1}+{m}_{2}+\dfrac{I}{{R}^{2}}\right){R}^{2}}=\omega }

\dfrac{1}{R}\sqrt{\dfrac{2\left({m}_{1}-{m}_{2}\right)gh}{\left({m}_{1}+{m}_{2}+\dfrac{I}{{R}^{2}}\right)}}

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JEE Main 2025 Apr 2 Shift 1 question paper

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