The diagram shows a fixed block with a horizontal top surface and a surface which is inclined at an angle of θ° to the horizontal, where sin θ = 3/5. A particle A of mass 0.3 kg rests on the horizontal surface and is attached to one end of a light inextensible string. The string passes over a small smooth pulley P fixed at the edge of the block. The other end of the string is attached to a particle B of mass 1.5 kg which rests on the sloping surface of the block. The system is released from rest with the string taut. [Figure X.X]

1. (i)Given that the block is smooth, find the acceleration of particle A and the tension in the string.[5]
2. (ii)It is given instead that the block is rough. The coefficient of friction between A and the block is μ and the coefficient of friction between B and the block is also μ. In the first 3 seconds of the motion, A does not reach P and B does not reach the bottom of the sloping surface. The speed of the particles after 3 s is 5 m s⁻¹. Find the acceleration of particle A and the value of μ.[9]

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