Question

Derive the relation between G and g

Answer 1

Newton's force of gravitational attraction between two bodies m1 and m2 separated by a distance d is:

 F = G m1 m2 /d²

The force of attraction with which planet Earth (of mass M and radius R) attracts a body of mass m on the surface of Earth is equal to its weight W.

    Weight = W = m g = Force = G M m/R²
    
  So g = G M / R²

Answer 2

As we know that: F = Gmm/r$r^{2}$

and F = m x g

so,             mg = Gmm/$r^{2}$

therefore,                   g = (G x m x m/$r^{2}$) x 1/m

cancel out one m with one m

                       g = GM/$r^{2}$