A plank of uniform density and length L is placed on a level surface. A 500g mass is placed at a point one fifth of the way down the length of the plank and the non-weight end of the plank is extended over a sharp edge. At a point when two thirds of the plank has been extended the plank + weight system is perfectly balanced. What must the mass of the plank be for this system to balance at the given point? What is the center of mass of the plank + weight system in terms of L, the length of the plank?