One end of a light inextensible string is attached to a particle $$\(A\)$$ of mass $$\(5 \mathrm{~m}\)$$. The other end of the string is attached to a particle $$\(B\)$$ of mass $$\(3 \mathrm{~m}\)$$. The string passes over a small, smooth, light fixed pulley. Particle $$\(A\)$$ is held at rest with the string taut and the hanging parts of the string vertical, as shown in Figure 4. Particle $$\(A\)$$ is released. (a) Find, in terms of $$\(m\)$$ and $$\(g\)$$, the magnitude of the force exerted on the pulley by the string while $$\(A\)$$ is falling and before $$\(B\)$$ hits the pulley. (8) (b) State how, in your solution to part (a), you have used the fact that the pulley is smooth. (1)

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