A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N? What is the linear acceleration of the rope? Assume that there is no slipping.

A rope of negligible mass is wound round a hollow cylinder of mass 3 k

1.	A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N? What is the linear acceleration of the rope? Assume that there is no slipping.
Answer» EXPLANATION:Here, Mass of HOLLOW cylinder (m) = 3kg Radius ( r) = 40 cm Force (F) = 30 N Moment of inertia of hollow sphere about its axis of symmetry ( I) = mr² = 3 × (0.4)² = 0.48 Kg.m² TORQUE acting on cylinder by applied force = r× F = 30 × 0.4 = 12N.m Angular acceleration produced in cylinder , angular acceleration = torque /M.O.I = 12/0.48 = 25 rad/s² Linear acceleration = angular acceleration × radius = 0.4 × 25 = 10 m/s²

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A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N? What is the linear acceleration of the rope? Assume that there is no slipping.​​

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A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N? What is the linear acceleration of the rope? Assume that there is no slipping.