# 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