A particle of mass $$\(10 \mathrm{~kg}\)$$ is placed on a fixed rough inclined plane. The plane is inclined to the horizontal at an angle $$\(\alpha\)$$, where $$\(\tan \alpha=\frac{3}{4}\)$$. The particle is held in equilibrium by a force of magnitude $$\(P\)$$ newtons, which acts up the plane, as shown in Figure 1. The line of action of the force lies in a vertical plane that contains a line of greatest slope of the plane. The coefficient of friction between the particle and the plane is $$\(\frac{1}{2}\)$$. (a) Find the normal reaction between the particle and the plane. (2) (b) Find the greatest possible value of $$\(P\)$$. (4) (c) Find the least possible value of $$\(P\)$$. (2)

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