[UPSC CSE 1998] Rigid Body Dynamics (Q243, 20M)

A block A of mass 6\text{ kg} is placed on a plane inclined to the horizontal at an angle 30^\circ. It is joined to another block B of mass 18\text{ kg} by means of a massless string going round a pulley. B hangs vertically. The pulley can be approximated as a uniform circular disc of mass 2\text{kg} and radius 10\text{cm}. The string from A to the pulley is parallel to the plane. The kinetic friction coefficient is \frac{1}{3\sqrt{3}}. Calculate the acceleration of B and the tensions in the two segments of the string.