A uniform ladder, AB, has one end, A, on smooth horizontal ground. The other end, B, rests against a smooth vertical wall. The ladder is modelled as a uniform rod of mass m and length 4a. The ladder is kept in equilibrium by a horizontal force, F, acting at a point C of the ladder, where AC = a. The force,F, and the ladder lie in a vertical plane perpendicular to the wall. The ladder is inclined to the horizontal at angle of 0, where tan 0 = 2. Find F in terms of m and g.