Newton’s laws of motion are applicable to point objects. The introduction of the concept of centre of mass enables us to apply them equally well to the motion of finite or extended objects.
The centre of mass of a body is a point where the whole mass of the body is supposed to be concentrated for describing its translatory motion.
The centre of mass of a system of particles is that single point which moves in the same way in which a single particle having the total mass of the system and acted upon by the same external force would move.
If a single force acts on a body and the line of action of the force passes through the centre of mass, the body will have only linear acceleration and no angular acceleration.
For example, consider a hammer resting on a plane surface.
>>If a force P is applied on the hammer in such a way that its line of action passes through the centre of mass of the hammer, then the hammer moves along a straight line path.
>>But when a force R is applied along a line not passing through its centre of mass, then the hammer rotates about its centre of mass.
Centre of mass vs. centre of gravity:
Let us understand how centre of mass is different from centre of gravity.
The centre of mass of body is point where whole mass of the body may be assumed to be concentrated for describing its translatory motion. On the other hand, the centre of gravity is a point at which the resultant of the gravitational forces on all the particles of the body acts i.e., a point where whole weight may be assumed to act.
In a uniform gravitational field such as that of the earth on a small body, the centre of gravity coincides with the centre of mass. But in the case of Mount Everest, the centre of gravity lies a little below its centre of mass because the gravitational force decreases with altitude.