Question

What units must the constant G have in order for the u it’s F to be newtons (N)?

Answer 1

The units for G must be $[N][m^2][kg^{-2}]$

Explanation:

The magnitude of the gravitational force between two objects is given by:

$F=G\frac{m_1 m_2}{r^2}$

where

F is the force

G is the gravitational constant

$m_1, m_2$ are the masses of the two objects

$r$ is the separation between the objects

We know that:

• The units of F are Newtons (N)
• The units of $m_1,m_2$ are kilograms (kg)
• The units of $r$ are metres (m)

So, we can rewrite the equation in terms of G, to find its units:

$G=\frac{Fr^2}{m_1 m_2}=\frac{[N][m]^2}{[kg][kg]}=[N][m^2][kg^{-2}]$

Learn more about gravitational force:

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