Question

Newton's law of universal gravitation is represented by f = g mm r2 where f is the gravitational force, m and m are masses, and r is a length. force has the si units kg · m/s2. what are the si units of the proportionality constant g?

Answer 1

Answer: ${kg^{-1}}{s^{-2}}m^3$

$F=G \frac {mM}{R^2}$

force has the SI units:

$kg . ms^{-2}$

SI unit of mass is kg and SI unit of distance is m.

we can bring gravitational constant on one side of the formula and rest all the other terms on right hand side

$G= \frac {F}{mM}\times R^2=\frac{kg . ms^{-2}}{kg^2} \times m^2\\ = {kg^{-1}}{s^{-2}}m^3$