A wedge of mass M and height it has smooth surfaces. It is at rest on a smooth and horizontal oor. A particle of mass m slides down from the top of an inclined surface on the wedge. Given that the surface has an inclination angle gt to the horizontal. (a) Find the distance moved by the wedge when the particle is just at the bottom of the wedge. . (b) Find the speed of the wedge when the particle is just at the bottom of the wedge. Find also the speed of the particle relative to the wedge when the particle is just at the bottom of the wedge. [Hintz Consider the conservation of momentum and mechanical energy] (c) Find the time when the particle reaches the bottom of the wedge. (d) Repeat part (a) when the inclined surface is slightly rough