Consider a body of mass m on the surface of the Earth as shown in the Figure. Its distance from the centre of the Earth is R (radius of the Earth).

The gravitational force experienced by the body is **F = GMm/R ^{2}, **where M is the mass of the Earth.

From Newton’s second law of motion. Force F = mg.

Equating the above two forces, **GMm/R ^{2} = mg**

So, **g = GM/R ^{2}**

This equation shows that g is independent of the mass of the body rn. But, it varies with the distance from the centre of the Earth. If the Earth is assumed to be a sphere of radius R, the value of g on the surface of the Earth is given by **g = GM/R ^{2.}**