A ladder AB of weight W and length l is held in equilibrium by a horizontal force P as shown in the figure given above. Assuming the ladder to be idealized as a homogeneous rigid bar and the surfaces to be smooth, which one of the following is correct ?

ANS:A -

Total horizontal force=0 implies Na = P.
Total vertical force=0 implies W = Nb.
This Na and Nb are normal force about the walls A and B.
The resultant force of Na perpendicular to the ladder at A is = Na(cosθ).
The resultant force of W perpendicular to the ladder is= W(sinθ).
Therefore Total momentum about B is 0
Which implies; Na(cosθ)L - W(sinθ)L/2 = 0.
Na = p = W/2 (tanθ).