A particle $$\(P\)$$ of mass $$\(4 m\)$$ lies on the surface of a fixed rough inclined plane. The plane is inclined to the horizontal at an angle $$\(\alpha\)$$ where $$\(\tan \alpha=\frac{3}{4}\)$$ The particle $$\(P\)$$ is attached to one end of a light inextensible string. The string passes over a small smooth pulley that is fixed at the top of the plane. The other end of the string is attached to a particle $$\(Q\)$$ of mass $$\(m\)$$ which lies on a smooth horizontal plane. The string lies along the horizontal plane and in the vertical plane that contains the pulley and a line of greatest slope of the inclined plane. The system is released from rest with the string taut, as shown in Figure 4, and $$\(P\)$$ moves down the plane. The coefficient of friction between $$\(P\)$$ and the plane is $$\(\frac{1}{4}\)$$ For the motion before $$\(Q\)$$ reaches the pulley (a) write down an equation of motion for $$\(Q\)$$, (1) (b) find, in terms of $$\(m\)$$ and $$\(g\)$$, the tension in the string, (7) (c) find the magnitude of the force exerted on the pulley by the string. (4) (d) State where in your working you have used the information that the string is light. (1)

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