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 centre. The magnitudes of the acceleration experienced by the blocks i $s____$ (assume no slipping of string on pulley.)

Question

G1 Physics · Accepted Answer

Let the pulley radius be r. Moment of inertia of the thin rim about its centre: I(rim) = Mr². Each rod has length 2r and mass M. For one rod about an axis through its centre and perpendicular to its length, I(rod) = M(2r)²/12 = Mr²/3. There are two rods, so I(pulley) = Mr² + 2(Mr²/3) = (5/3)Mr². Let the acceleration magnitude of the blocks be a, with block M moving downward. For block M: Mg - T₂ = Ma. (1) For block m: T₁ - mg = ma. (2) For the pulley, (T₂ - T₁)r = Iα. Because there is no slippi…