The units for G must be [tex][N][m^2][kg^{-2}][/tex]
Explanation:
The magnitude of the gravitational force between two objects is given by:
[tex]F=G\frac{m_1 m_2}{r^2}[/tex]
where
F is the force
G is the gravitational constant
[tex]m_1, m_2[/tex] are the masses of the two objects
[tex]r[/tex] is the separation between the objects
We know that:
- The units of F are Newtons (N)
- The units of [tex]m_1,m_2[/tex] are kilograms (kg)
- The units of [tex]r[/tex] are metres (m)
So, we can rewrite the equation in terms of G, to find its units:
[tex]G=\frac{Fr^2}{m_1 m_2}=\frac{[N][m]^2}{[kg][kg]}=[N][m^2][kg^{-2}][/tex]
Learn more about gravitational force:
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