When does a body (system) have different centre of gravity and centre of mass?

Write the difference between centre of gravity and centre of mass of a body?

Define centre of mass.

Find the distance between centre of gravity and centre of mass of a two particle system attached to the ends of a light rod. Each particle has same mass. Length of the rod is R, where R is the radius of earth.

Write short note on centre of Gravity.

Satement-1: if there is no external torque on a body about its centre of mass, then the velocity of the center of mass remains constant. Statement-2: The linear momentum of an isolated system remains constant.

The multiplication of total mass of system and the acceleration of its centre of mass denote what?

The centre of gravity of a body on the earth coincides with its centre of mass for a small object whereas for an extended object it may not. What is the qualitative meaning of small and extended in this regard? For which of the following two coincides? A building, a pond, a lake, a mountain?

A double star is a system of two stars of masses m and 2m , rotating about their centre of mass only under their mutual gravitational attraction. If r is the separation between these two stars then their time period of rotation about their centre of mass will be proportional to