### Q.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.

**Answer:-**

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* = *mr*^{2}

= 3 × (0.4)^{2} = 0.48 kg m^{2}

Torque, τ = *F* × *r* = 30 × 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 }