The gravitational force \( F \) between two masses is given by Newton's law of gravitation:
\[ F = G \frac{m_1 m_2}{r^2} \]
Where:
- \( F \) is the gravitational force in newtons (N),
- \( G \) is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses in kilograms (kg),
- \( r \) is the distance between the centers of the two masses in meters (m).
To find the units of the gravitational constant \( G \), we can rearrange the formula:
\[ G = F \frac{r^2}{m_1 m_2} \]
Now we need to express the units for \( G \):
- The units of force \( F \) are newtons (N).
- The units of distance \( r \) are meters (m), thus \( r^2 \) will have units of \( m^2 \).
- The units for masses \( m_1 \) and \( m_2 \) are kilograms (kg), so their product \( m_1 m_2 \) will have units of \( kg^2 \).
Substituting these units into the expression for \( G \):
\[ [G] = \frac{[F][r^2]}{[m_1][m_2]} = \frac{N \cdot m^2}{kg \cdot kg} = \frac{N \cdot m^2}{kg^2} \]
Thus, the units for the gravitational constant \( G \) must be:
\[ \text{N} \cdot \text{m}^2/\text{kg}^2 \]
The correct answer is therefore:
N x m²/kg²