Two particles, $$\(A\)$$ and $$\(B\)$$, have masses $$\(2 \mathrm{~kg}\)$$ and $$\(4 \mathrm{~kg}\)$$ respectively. The particles are connected by a light inextensible string. The string passes over a small smooth pulley which is fixed at the top of a rough plane. The plane is inclined to the horizontal ground at an angle $$\(\alpha\)$$ where $$\(\tan \alpha=\frac{3}{4}\)$$. The particle $$\(A\)$$ is held at rest on the plane at a distance $$\(d\)$$ metres from the pulley. The particle $$\(B\)$$ hangs freely at rest, vertically below the pulley, at a distance $$\(h\)$$ metres above the ground, as shown in Figure 3. The part of the string between $$\(A\)$$ and the pulley is parallel to a line of greatest slope of the plane. The coefficient of friction between $$\(A\)$$ and the plane is $$\(\frac{1}{4}\)$$ The system is released from rest with the string taut and $$\(B\)$$ descends. (a) Find the tension in the string as $$\(B\)$$ descends. (9) On hitting the ground, $$\(B\)$$ immediately comes to rest. Given that $$\(A\)$$ comes to rest before reaching the pulley, (b) find, in terms of $$\(h\)$$, the range of possible values of $$\(d\)$$. (7) (c) State one physical factor, other than air resistance, that could be taken into account to make the model described above more realistic. (1)

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