A uniform thin rod of mass M and length L is standing vertically along the y-axis on a smooth horizontal surface, with its lower end at the origin (0,0). A slight disturbance at t=0 causes the lower end to slip on the smooth surface along the positive x-axis, and the rod starts falling.
(i) What is the path followed by the centre of mass of the rod during its fall?
(ii) Find the equation to the trajectory of a point on the rod located at a distance r from the lower end. What is the shape of the path of this point?