Hint: center of gravity (CG) of a body is a point at which the entire weight of the body concentrates. Centre of the mass (CM) coincides with the center gravity (CG) only when the mass is distributed uniformly over the body. The gravitational field acting on the body can be calculated by considering the body as a point mass.
The Centre of gravity of a body is defined as the point where the whole weight of the body is supposed to act. A body supported at its center of gravity remains balanced and it is in mechanical equilibrium. The reaction R at the point of support is equal and opposite to the total weight MG of the body. Hence, there is a translational equilibrium. Also, the total gravitational torque on the body at the center of gravity is zero. Hence, there is a rotational equilibrium. The center of gravity of the body coincides with the center of mass in uniform gravity (constant value of acceleration due to gravity)or gravity-free space.
the remaining two statements are wrong. The radius of gyration of a body about an axis is defined as the distance from the axis of rotation to the mass point whose mass is equal to the mass of the whole body and whose moment of inertia is equal to the moment of inertia of the whole body about the same axis.