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A rope of negligible mass is wound around a hollow cylinder of mass 3 kg and radius 40 cm and then the entire arrangement is placed on a smooth horizontal surface. What is the angular acceleration (in rad s-2) of the cylinder if the rope is pulled with a  force of 30 N?
PhysicsRotational MotionJEE Main
Solution:
1583 Upvotes Verified Answer
The correct answer is: 10
Given,              M = 3 kg

                        R = 40 cm = 0.40 m

                        F = 30 N

Moment of inertia of the hollow cylinder about its axis of symmetry

                         I = MR2

                           = 3 × (0.40)2 = 0.48 kg-m2

Torque acting on the cylinder by the applied force,

                          τ = F × R

                           = 30 × 0.40 = 12 N-m.

Angular acceleration produced in cylinder,

α = τ I = 12 0.48 = 25 rad/s 2

Linear acceleration, a = R α

                           = 0.40 × 25 = 10.0 m/s2

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