A rope of length L and mass per unit length `lambda` passes over a disc shaped pulley of mass M and radius R. The rope hangs on both sides of the pulley and the length of larger hanging part is `l`. The pulley can rotate about a horizontal axis passing through its centre. The system is released from rest and it begins to move. The pulley has no friction at its axle and the rope has large enough friction to prevent it from slipping on the pulley.
(a) Find the acceleration of the rope immediately after it is released.
(b) Find the horizontal component of the force applied by the axle on the pulley immediately after the system is released

Answer

(a) `(lambda g(2l + pi R - L))/((lambda L + (M)/(2))`