Three points A, B and C lie on a line of greatest slope of a plane inclined at an angle of 30° to the horizontal, with AB = 1 m and BC = 1 m, as shown in the diagram. A particle of mass 0.2 kg is released from rest at A and slides down the plane. The part of the plane from A to B is smooth. The part of the plane from B to C is rough, with coefficient of friction μ between the plane and the particle.

\((a) Given that μ = \frac{1}{2}\sqrt{3}, find the speed of the particle at C.\)

(b) Given instead that the particle comes to rest at C, find the exact value of μ.