Answer to Question #217528 in Mechanics | Relativity for IBHD

Question

Newton's law of universal gravitation gives the force between two objects of mass 1 and mass 2 separated by distance how as F=G(M1 M2)/R2 use dimensional analysis to find the unit of gravitational

Answer 1

Gravitational force acting between two objects of masses m₁ and m₂ separated by distance r, 

$F = \frac{Gm_1m_2}{r^2}$

⟹ $G = \frac{Fr^2}{m_1m_2}$

Thus dimensional formula of G is $\frac{[MLT^{-2}][L^2]}{[M^2]}$

⟹ $G = M^{-1}L^3T^{-2}$