Why centre of mass equal to centre of gravity

Because mass and distance determine gravity, so the more mass you have, the more gravity.

Hopefully this helps you The center of gravity is based on weight, whereas the center of mass is based on mass. So, when the gravitational field across an object is uniform, the two are identical. ... More practically, the COG is the point over which the object can be perfectly balanced; the net torque due to gravityabout that point is zero.

Iwannasay c is the most accurate

One splits the atoms and molecules  the other combines them