Two particles, \(A\) and \(B\), of masses \(0.5\text{ kg}\) and \(0.8\text{ kg}\) respectively are attached to the ends of a light inextensible string. The string passes over a small smooth pulley fixed at the end of a rough horizontal plane and to the top of a smooth inclined plane. Particle \(A\) is held on the horizontal plane, while \(B\) lies on the inclined plane, which makes an angle of \(55^\circ\) with the horizontal. The string is in the same vertical plane as a line of greatest slope of the inclined plane (see diagram).

Particle \(A\) is released from rest with the string taut. Particle \(B\) moves \(0.3\text{ m}\) down the inclined plane in \(0.4\text{ s}\).

(a) Find the tension in the string.

(b) Find the coefficient of friction between \(A\) and the horizontal plane.

(c) After \(B\) has been moving for \(0.4\text{ s}\), the string suddenly breaks. Given that \(A\) subsequently comes to rest on the horizontal plane, find the work done by the frictional force in bringing \(A\) to rest.

You may assume that \(A\) does not reach the pulley.