The wedge shown can slide without friction on a horizontal floor. Mass of the wedge is M and its angle of inclination is $\theta ={30}^0.$ A block of mass m slides down the wedge without friction when released on its inclined face. If path of the block relative to the ground makes an angle of $\varphi ={60}^0$ with the horizontal, find the ratio of mass of the block to that of the wedge.