A cube of mass m is placed on top of a wedge of mass 2 m , as shown in figure. There is no friction between the cube and the wedge. The minimum co-efficient of friction between the wedge and the horizontal surface, so that the wedge does not move is

Step-by-step solution

The normal reaction between the wedge and the block is N ' = m g cos θ So the net horizontal force on the wedge is F = m g cos ⁡ θ sin ⁡ θ The normal reaction between the wedge and the ground is N = 2   m g + m g cos 2 ⁡ θ N = 2   m g + m g   c o s 2 θ Now, F = μ N gives μ = F N = m g cos ⁡ θ sin ⁡ θ 2   m g + m g cos 2 ⁡ θ = cos ⁡ θ sin ⁡ θ 2 + cos 2 ⁡ θ For θ = 45 o , &#1