A meter stick is placed vertically at the origin on a frictionless surface. A gentle push in +x direction is given to the topmost point of the rod when it has fallen completely x coordinate of center of the rod is at:
Since there us no external force on the rod, the center of mass of the rod will not move in horizontal direction.
In vertical direction, we have gravitational force as an external force so com of rod will come 0.5m down, but will not move in x direction.
So COM will be the origin.
Thus option A is correct.