Centre of Gravity:

If there is a system of n elements with masses m₁, m₂, ..., m_n on a xy-plane with co-ordinates (x₁, y₁), (x₂, y₂), ...., (x_n, y_n) respectively. Then the co-ordinates  of the centre of mass or centre of gravity or centroid of the system are shown by

For a continuous element of mass M, the co-ordinates of the C.G. of the body are shown by substituting the summations in (1) by integration, such that

Where Δm is the infinitesimal of the general particle of the body whose C.G. is at the point (x, y).