Centre of mass is a point of the body which represents entire motion of body. It may have mass content at that point or not but it represent the actual motion of the body. For a regular body centre of mass and centre of gravity coincide together.
Let the distances of the two particles be x1 and x2 respectively from some origin O. Let m1 and m2 be respectively the masses of the two particles. The centre of mass of the system is that point C which is at a distance X from O, where X is given by
Example :A projectile, following the usual parabolic trajectory, explodes into fragments midway in air. The forces leading to the explosion are internal forces. They contribute nothing to the motion of the centre of mass. The total external force, namely, the force of gravity acting on the body, is the same before and after the explosion.
The centre of mass under the influence of the external force continues, therefore, along the same parabolic trajectory as it would have followed if there were no explosion.
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