A thin uniform equilateral plate rests in a vertical plane with one of its vertex A on a rough horizontal floor and another vertex B on a smooth vertical wall. If the coefficient of friction μ = 1 3 , then the least angle θ its base AB can make with the horizontal surface is

Step-by-step solution

Let us assume that the side-length of the triangle is a , then l = a 3 N 1 = M g f 1 = μ N 1 = N 2 N 2 = μ M g Balancing the torque about point A M g × l cos 30 ° + θ - N 2 × a sin θ = 0 ⇒ M g × a 3 cos 30 ° + θ - μ M g × a sin θ = 0 1 3 3 2 cos θ - 1 2 sin θ = μ sin θ On solving further we get θ = cot - 1 2 μ + 1 3