A uniform ladder $AB$, with length 4 m and mass 12 kg, rests with its end $A$ on rough horizontal ground. The ladder is in limiting equilibrium against a fixed smooth horizontal rail at a point $C$, where $AC=3$ m. The ladder is in a vertical plane perpendicular to the rail and is inclined to the horizontal at an angle $\alpha$, where $\tan \alpha =4/3$. The coefficient of friction between the ladder and the ground is $\mu$.