System of particles and Rotational motion NCERT Solutions Class 11 Physics - Solved Exercise Question 7.14

Question 7.14:

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.

Solution:

Mass of the hollow cylinder, m = 3 kg
Radius of the hollow cylinder, r = 40 cm = 0.4 m
Applied force, F = 30 N
The moment of inertia of the hollow cylinder about its geometric axis:
I = mr²
= 3 × (0.4)² = 0.48 kg m²
Torque, τ = F X r  =  30 X 0.4  = 12 Nm
For angular acceleration α, torque is also given by the relation:
τ = Iα
α = τ / I  =  12 / 0.48  = 25 rad s^-2
Linear acceleration = τα = 0.4 × 25 = 10 m s^–2