Question

Which of the following represents the correct dimensions of the gravitational constant?

• A. $\left[M^{-1}{L}^3{T}^{-2}\right]$
• B. $\left[ML{T}^{-1}\right]$
• C. $\left[M{L}^{-1}{T}^{-2}\right]$
• D. $\left[M{L}^{-2}{T}^{-2}\right]$

Answer 1

The correct option is A $\left[M^{-1}{L}^3{T}^{-2}\right]$

As we know that the force due to gravitation is given as
$F=\frac{G{m}_1{m}_2}{r^2}$, where $G$ is the gravitational constant.
So, we have
$G=\frac{F{r}^2}{m_1{m}_2}$
$\Rightarrow \left[G\right]=\frac{\left[ML{T}^{-2}\right]\left[L^2\right]}{\left[M\right]\left[M\right]}=\left[M^{-1}{L}^3{T}^{-2}\right]$