A rope is wound around 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` ?

Options

A. `10 rad/s^(2)`
B. `15 rad/s^(2)`
C. `20 rad/s^(2)`
D. `25 rad/s^(2)`

Answer

D

Explanation

Moment of inertia of the hollow cylinder about its axis .
`= MR^(2) = 3.0 xx (0.4)^(2)`
= 0.48 `kgm^(2)`
Torque applied on the cylinder
`tau = "force" xx " momentum"`
`= 30 xx 0.40 = 12 N-m`
Angular acceleration `(alpha)` of the cylinder .
`alpha =(tau)/(l) = (12)/(0.48)`
`= 25 rad//s^(2)`