Question

Which of the following units can be used to express G?

• A. N Kg${}^{-2}$
• B. Nm${}^{-2}$ Kg${}^2$
• C. Nm${}^2$ Kg${}^{-2}$
• D. Nm${}^{-2}$ Kg${}^{-3}$

Answer 1

The correct option is C Nm${}^2$ Kg${}^{-2}$

Gravitational force between two masses $m$ and $M$, separated by a distance $r$ is given by $F=\frac{GMm}{r^2}$

Thus, $G=\frac{F{r}^2}{Mm}$

We know that the unit of force ($F$) is newton (N), the unit of mass ($morM$) is kg and the unit of distance ($r$) is meter(m).

$\text{The unit of G}=\frac{N{m}^2}{k{g}^2}=N{m}^{2}k{g}^{-2}$