Question

Obtain a relationship between g and G

Answer 1

one of the relationship is that they both are same alphabet

Answer 2

F=(Gxm1xm2)/r^2

M1 be mass of earth
M2 be mass of object
F will be force experienced by object
F = M2 x (acceleration)

Therefore
m2 x g = (Gxm1xm2)/r^2

g = (Gxm1)/r^2

Here acceleration is g
G is gravitational constant
6.673 x 10^-11 N m^2 / kg^2