Problem 1.138

A horizontal plane supports a stationary vertical cylinder of radius $R$ and a disc $A$ attached to the cylinder by a horizontal thread $A B$ of length $l_{0}$ (Fig. 1.32, top view). An initial velocity $v_{0}$ is imparted to the disc as shown in the figure. How long will it move along the plane until it strikes against the cylinder? The friction is assumed to be absent.