The diagram shows the cross-section OABCDE through the centre of mass of a uniform prism on a rough inclined plane. The portion ADEO is a rectangle in which AD = OE = 0.6m and DE = AO = 0.8m; the portion BCD is an isosceles triangle in which angle BCD is a right angle, and A is the mid-point of BD. The plane is inclined at 45° to the horizontal, BC lies along a line of greatest slope of the plane and DE is horizontal.

i. Calculate the distance of the centre of mass of the prism from BD. The weight of the prism is 21 N, and it is held in equilibrium by a horizontal force of magnitude P N acting along ED.

ii. a. Find the smallest value of P for which the prism does not topple.

b. It is given that the prism is about to slip for this smallest value of P. Calculate the coefficient of friction between the prism and the plane. 

The value of P is gradually increased until the prism ceases to be in equilibrium.

iii. Show that the prism topples before it begins to slide, stating the value of P at which equilibrium is broken.