Question

If force $F$, energy $E$, length $L$ and time $T$ are taken as fundamental quantities. The dimensional formula of gravitational constant is

• A. $E^3{F}^{-1}{L}^6{T}^5$
• B. $F{L}^6{E}^{-2}{T}^{-4}$
• C. $E^{2}F{L}^6{T}^3$
• D. $FE{L}^5{T}^{-1}$

Answer 1

The correct option is B $F{L}^6{E}^{-2}{T}^{-4}$

The dimension of used quantities is,
Force $\left[F\right]=\left[M^1{L}^1{T}^{-2}\right]$

Energy $\left[E\right]=\left[M{L}^2{T}^{-2}\right]$

Length $\left[L\right]=\left[L\right]$

Time $\left[T\right]=\left[T^1\right]$

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

Dimension of mass in term of energy is given as,
$\left[M\right]=\left[E{L}^{-2}{T}^2\right]$

We use the formula of gravitational force,
$F=\frac{G{m}_1{m}_2}{r_2}$

$\left[G\right]=\frac{F{r}^2}{m_1{m}_2}=\left[F{L}^2{M}^{-2}\right]$

put the dimensions of quantity,
$\left[F{L}^2\right]{\left[E{L}^{-2}{T}^2\right]}^{-2}=\left[F{L}^6{E}^{-2}{T}^{-4}\right]$