Derive a relation between Universal Gravitational Constant (G) and Acceleration due to gravity (g) ?

suppose earth is a soid sphere which will attract the body towards its centre. So, acc. to law of gravitation force on the body will be,

F=G*m1m2/R^2

but we now that F=ma

and here accleration (a) = accleration due to gravity (g), so

force applied by earth on will also be mg

replace above F in formula by mg and solve,

F=G*mE*m/R^2 (here mE is mass of earth and m is mass of body)

mg=G*mEm/R^2

so,

g = G*mE/R^2

Suppose earth is a soid sphere which will attract the body towards its centre. So, acc. to law of gravitation force on the body will be,

F=G*m1m2/R^2

but we now that F=ma

and here accleration (a) = accleration due to gravity (g), so

force applied by earth on will also be mg

replace above F in formula by mg and solve,

F=G*mE*m/R^2 (here mE is mass of earth and m is mass of body)

mg=G*mEm/R^2

so,

g = G*mE/R^2