Statements :
a) Position of centre of mass depends on acceleration due to gravity where as position of centre of gravity independent on acceleration due to gravity.
b) Centre of gravity of a body is defined to know the amount of stability of the body and the center of mass of the body is defined to describe the nature of motion of the body.

Position of centre of mass depends upon the distribution of mass and geometry of the system. Position of COM determines the nature of motion (rotational or translation) of a body under the action of external forces.

Centre of gravity is the point of action of resultant gravitational force acting on the system. Position of centre of gravity determines the stability of a body. So (a) is wrong and (b) is right.