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\includegraphics[max width=\textwidth, alt={}, center]{610c1d96-3833-4a71-a71c-4cac13982332-12_365_831_264_657} The diagram shows a triangular block with sloping faces inclined to the horizontal at \(45 ^ { \circ }\) and \(30 ^ { \circ }\). Particle \(A\) of mass 0.8 kg lies on the face inclined at \(45 ^ { \circ }\) and particle \(B\) of mass 1.2 kg lies on the face inclined at \(30 ^ { \circ }\). The particles are connected by a light inextensible string which passes over a small smooth pulley \(P\) fixed at the top of the faces. The parts \(A P\) and \(B P\) of the string are parallel to lines of greatest slope of the respective faces. The particles are released from rest with both parts of the string taut. In the subsequent motion neither particle reaches the pulley and neither particle reaches the bottom of a face.

1. Given that both faces are smooth, find the speed of \(A\) after each particle has travelled a distance of 0.4 m .
2. It is given instead that both faces are rough. The coefficient of friction between each particle and a face of the block is \(\mu\). Find the value of \(\mu\) for which the system is in limiting equilibrium. [6]
   If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.