Question

What is the dimensional formula of universal gravitational 'G'? The gravitational force of attraction between two objects of masses $m_{1}and{m}_2$ seperated by a distance d is given by $F=\frac{G{m}_1{m}_2}{d_2}$. Where 'G' is the universal gravitational constant.

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

Answer 1

Answer: (C)

$\left[M^{-1}{L}^3{T}^{-2}\right]$

Gravitational constant can be written as $G=\frac{F{r}^2}{m_1{m}_2}$

So, its dimensions are $\left[G\right]=\frac{\left[F\right]\left[r^2\right]}{\left[m_1\right]\left[m_2\right]}$

$⟹\left[G\right]=\frac{\left[ML{T}^{-2}\right]\left[L^2\right]}{\left[M\right]\left[M\right]}=\left[M^{-1}{L}^3{T}^{-2}\right]$