Centre of Mass:

This is the point where the whole mass of a body may be supposed to be concentrated. The centre of mass and the centre of gravity of a body are different just while the gravitational field is not uniform and parallel. For most practical purposes they are supposed to be the similar.

The concept of centre of gravity & centre of mass are further explained as given below. A body may be considered like an agglomeration of a large number of particles each of which is adhering to its adjacent particles. These particles can have different sizes, density or can have consistent size and density. Each of these particles is subjected to gravitational force directed towards the centre of the earth. The magnitude of the gravitational force shall base on its mass. For all of the earthly bodies whose sizes are extremely small as compared to its distance up to the centre of the earth, the forces of gravitational attraction on several particles of the body may be supposed to be parallel. Therefore the total weight of the body is the summation of all of these parallel forces acting vertically down towards the centre of the earth. Therefore, the line of action of the resultant R (total weight) of these forces can be found.

Let a case of a triangular metal plate ABC placed in a vertical plane with its side AB vertical. If you divide the area of the triangle into large number of imaginary vertical strips parallel to BA, then for each f the strip the gravitational force may be computed and resultant R of all these forces shall lie along a vertical line (1-G) as illustrated in Figure (a), where G is a point in which whole weight of the plate is concentrated. While the plate is oriented at right angle to its earlier position, line BC is placed vertically as illustrated in Figure (b). New vertical strips may be formed and resultant R that is obviously of same magnitude R as in the case of first orientation (a), shall lie along vertical line (2-G). The location of G shall be the intersection of lines of action of the resultants obtained in cases (a) and (b). The mass centre is a unique point G in the plate ABC through that the resultant weight of all of the strip-masses shall always pass through irrespective of the orientation of the plate. Figure illustrated the third orientation of triangle ABC where one of the medians BGB′ in the triangle is kept vertical. It may be illustrated that the point of intersection of all the medians represents the mass-centre of the triangular plate.

Figure : Position of Resultant R for Different Orientations of Plate ABC

Centre of gravity or Mass-centre is a point in the body whereas whole mass or weight is supposed to be concentrated and for convenience single resultant gravity load R may be used as a replacement for distributed gravity loads at several locations of its particles.