A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. If the rope is pulled with a force of 30 N, then the angular acceleration produced in the cylinder is

Explanation

`m=3kg, r = 40 cm = 0.40 m`, Force F = 30 N
Angular acceleration `= alpha`= ?
`tau = I alpha, tau = F xx r, Fr = Ialpha`
M.I. of the hollow cylinder about its axis, `I = mr^(2)`
`alpha = (Fr)/(mr^(2)) = (30 xx 0.4)/(3 xx 0.4 xx 0.4) = 25 "rad" s^(-2)`
Linear acceleration = a= ?
`a= ralpha`
`= 0.4 xx 25 ~~ 10 ms^(-2)`