Two identical ladders are arranged as shown in the figure. Mass of the block is m and the mass of each ladder is M . The length of each of the ladder is L . The system is in equilibrium. What is the magnitude of frictional force acting at A or B ?

Step-by-step solution

Drawing force diagrams of the rod, we have This is the equilibrium of coplanar forces, hence using the equations ∑ F x = 0 , ∑ F y = 0 and Net moment about point O = 0 we have the equations, N + N 2 = M g + m g 2 ... (i) N 1   =   f ...(ii) N   =   N 2 + M g + m g 2 ... (iii) and M g L 2   cos   θ   +   f L sin   θ   =   N L cos   θ   ... (iv) Solving these four equations, we have f ⁡ = M + m 2 g cot θ