Question

A rope is wound around a solid cylinder of mass 1 kg and radius 0.4 m. What is the angular acceleration of cylinder, if the rope is pulled with a force of 25 N? (Cylinder is rotating about its own axis.)

Options

• 125 rad/s²

• 10 rad/s²

• 1 rad/s²

• 50 rad/s²

Answer 1

125 rad/s²

Explanation:

Consider the free body diagram shown below,

The torque about centre of cylinder,

τ = F × r = 25 × 0.4 = 10 Nm

The relation between angular acceleration (α) and torque (τ) is given as

τ = kχ

`= "Mr"^2/2 alpha`  `("For solid cylinder, I" = "MR"^2/2)`

`10 = (1 xx (0.4)^2)/2 alpha`

⇒ α = 125 rad/s²