Derive the Dimensional Formula of Universal Constant of Gravitation?
Universal Constant of Gravitation is represented by G and is derived from Newton’s law of gravitation. Newton’s law states that
F=(Gm1m2)/r2
So
G=(Fr2)/m1m2
Where F is Force between masses m1, m2 at a distance r
Dimensional Formula of Force= M1L1T-2
Thus
Dimensional Formula of Universal Constant of Gravitation= (M1L1T-2 x L2)/(M1 x M1)
Dimensional Formula of Universal Constant of Gravitation = M-1L3T-2
SI unit of Universal Constant of Gravitation is Nm2kg-2
or
Dimensional Formula of Gravitational constant = M-1L3T-2