A 13 m ladder is placed against a smooth vertical wall with its lower end 5m from the wall. What should be the minimum coefficient of friction between ladder and floor so that it remains in equilibrium.

vertical direction downward force mg and normal reaction on the floor  clockwise torque about the origin is mgx52 and anticlockwise torque μmg (12)   [12 is the height of the ladder]  as it is in equilibrium mg52 =μmg12 μ=524≈0.21