A uniform rod AB has weight 6N and length 0.8 m. The rod rests in limiting equilibrium with B in contact with a rough horizontal surface and AB inclined at 60° to the horizontal. Equilibrium is maintained by a force, in the vertical plane containing AB, acting at A at an angle of 45° to AB (see diagram). Calculate

i. The magnitude of the force applied at A,

ii. The least possible value of the coefficient of friction at B.