Answer to Question #100254 in Physics for Lad

Question

The force of attraction F between two masses m and m separated by a distance g is given as F= (Gmm) ÷g×g where G is the universal gravitational constant. Use dimensions to derive S.I units of G

Answer 1

$$[F]=[G][m]^2[r]^{-2}$$

$$kg\cdot m\cdot s^{-2}=[G]kg^2\cdot m^{-2}$$

Thus,

$$[G]=kg^{-1}\cdot m^{3}\cdot s^{-2}$$