Question

Given Newton's law of universal gravitation where F is the force between two masses objects, m1 and m2 are the masses of the two bodies and r is the distance between the two bodies. Determine the units of G in two ways 1) including Newtons, N, as one of the units and 2) not including N. (hint...if you don't recall what the dimensions of N are, think of Newton's second law!

Answer 1

a)
unit of F is N
unit of mass is kg
unit of r is m

put the unit in F = (G*m1*m2)/r^2
so,
N = (G*kg*kg)/m^2
G = (N*m^2)/(kg)^2

b)
also, we know that
dimension of N = (kg*m)/s^2
put this in above equation
so,
G = {((kg*m)/s^2)*m^2}/(kg^2)
= m^3/{(s^2)*(kg)}