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

A rope of negligible mass is wound round a hollow cylinder of mass 3 k

1.	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
Answer» Solution :`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)`