A string is wound around a hollow cylinder of mass 5 kg and radius 0.5 m. If the string is now pulled with a horizontal force of 40 N, and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular acceleration of the cylinder will be (Neglect the mass and thickness of the string)
(A)20rad/s2
(B)16rad/s2✓ Correct
(C)12rad/s2
(D)10rad/s2
Answer: (B)
Solution
Take torques about the line of contact with the ground, where friction contributes nothing. The string is pulled horizontally from the top of the cylinder, a height 2R above the contact line, so its torque is F⋅2R. The moment of inertia of the hollow cylinder about the contact line is MR2+MR2=2MR2 (its central value plus the parallel-axis shift). For rolling, F⋅2R=2MR2α, so α=MRF=5×0.540=16 rad/s2.
JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Single correct option