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, M = 3 kg

R = 40 cm = 0.4 m

M.I. of the hollow cylinder about its axis

= I = MR²

= 3 x (0.4)² = 0.48 kg m²

When the force of 30 N is applied over the rope wound round the cylinder, torque will act on the cylinder. It is given by,

τ = vector(F.R)

= 30 x 0.4 = 12 Nm

If α be the angular acceleration produced,

then, τ = Iα

or, α = τ/I = 12/0.48 = 25 rad s^-2.