Every particle of matter in a body is attracted to the Earth and the result of all these attractive forces is the weight of the body.
Let w1, w2...... be the weights of a large number of particles of object whose total weight is W.
Let the coordinates of each particle be (x1,y1), (x2,y2).
Then the moment of particle 1 is w1 x1, particle 2 is w2 x2
The total torque is
If the axes of reference are rotated by 90o, the total weight is unaltered. But,
If we divide (1) and (2) by g, the equations become identical to the definition of centre of mass.
The centre of gravity is the same as the centre of mass of any body.
