Question

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 1

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

Answer 2

Answer:

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

Explanation: