The pulley shown in figure is made using a thin rim and two rods of… | JEE Main 2026 (21 Jan, Shift 2)

Q10JEE Main 2026 · 21 JAN · SHIFT 2Difficult

Rotational Kinematics & Dynamics

The pulley shown in figure is made using a thin rim and two rods of length equal to diameter of the rim. The rim and each rod have a mass of M. Two blocks of mass of M and m are attached to two ends of a light string passing over the pulley, which is hinged to rotate freely in vertical plane about its center. The magnitudes of the acceleration experienced by the blocks is ________ (assume no slipping of string on pulley).

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Answer: (a)

Rim: $MR^2$ . Each rod (length $2R$ ) about its centre: $\dfrac{M(2R)^2}{12} = \dfrac{MR^2}{3}$ .
$I = MR^2 + 2\cdot\dfrac{MR^2}{3} = \dfrac{5}{3}MR^2$
$a = \dfrac{(M - m)g}{M + m + I/R^2} = \dfrac{(M - m)g}{\frac{8}{3}M + m}$
So the answer is (a).

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