A rough plane is inclined to the horizontal at an angle $$\(\alpha\)$$, where $$\(\tan \alpha=\frac{3}{4}\)$$ A particle $$\(P\)$$ of mass $$\(2 \mathrm{~kg}\)$$ is held in equilibrium on the plane by a horizontal force of magnitude $$\(X\)$$ newtons, as shown in Figure 2. The force acts in a vertical plane which contains a line of greatest slope of the inclined plane. (a) Show that when $$\(X=14.7\)$$ there is no frictional force acting on $$\(P\)$$ (3) The coefficient of friction between $$\(P\)$$ and the plane is 0.5 (b) Find the smallest possible value of $$\(X\)$$. (8)

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