Which of the following is the correct unit for the universal gravitational constant $G$?

Solution

1. Start with Newton's law of universal gravitation: $F=G\frac{m_1{m}_2}{r^2}$.
2. Rearrange the formula to solve for the gravitational constant: $G=\frac{F{r}^2}{m_1{m}_2}$.
3. Substitute the SI units for force (N), distance (m), and mass (kg) into the equation: $G=\frac{\text{N}\cdot {\text{m}}^2}{\text{kg}\cdot \text{kg}}$.
4. Simplify the expression to obtain the final unit: ${\text{N m}}^2/{\text{kg}}^2$.
5. Hence the answer is (A).