A uniform ladder rests against a perfectly smooth vertical wall and a rough horizontal floor. It makes an angle with the horizontal floor and is on the verge of slipping. The minimum coefficient of static friction between the ladder and the floor is :

Step-by-step solution

Let the weight of the ladder be W and its length be L . For translational equilibrium, the normal reaction from the floor N_ f balances the weight of the ladder: N_ f = W The normal reaction from the wall N_ w balances the static friction f from the floor: f = N_ w For rotational equilibrium, taking torque about the point of contact with the floor: The weight W acts at the center of the ladder, producing a torque W ( L 2 ) . The normal reaction from the wall N_ w produces an opposing torque N_ w (L ) . Equating the