Two particles P and Q, of masses 0.2 kg and 0.1 kg respectively, are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley at B which is attached to two inclined planes. Particle P lies on a smooth plane AB which is inclined at 60° to the horizontal. Particle Q lies on a plane BC which is inclined at an angle of θ° to the horizontal. The string is taut and the particles can move on lines of greatest slope of the two planes (see diagram).

(a) It is given that θ = 60, the plane BC is rough and the coefficient of friction between Q and the plane BC is 0.7. The particles are released from rest. Determine whether the particles move.

(b) It is given instead that the plane BC is smooth. The particles are released from rest and in the subsequent motion the tension in the string is \\(\sqrt{3} - 1 \\\) N. Find the magnitude of the acceleration of P as it moves on the plane, and find the value of θ.