Question

If the speed of light (c), acceleration due to gravity (g) and pressure (p) are taken as the fundamental quantities, then the dimension of gravitational constant is

• A. $c^2{g}^0{p}^{-2}$
• B. $c^0{g}^2{p}^{-1}$
• C. $c{g}^3{p}^{-2}$
• D. $c^{-1}{g}^0{p}^{-1}$

Answer 1

The correct option is B $c^0{g}^2{p}^{-1}$

Let [G] $\propto c^x{g}^y{p}^z$
by substituting the following dimensions :
[G] = $\left[M^{-1}{L}^3{T}^{-2}\right],\left[c\right]=\left[L{T}^{-1}\right],\left[g\right]=\left[L{T}^{-2}\right]$
$\left[p\right]=\left[M{L}^{-1}{T}^{-2}\right]$
compare the dimension of M, L and T on both sides
we can get x=0,y=2,z=1
$\therefore \left[G\right]\propto c^0{g}^2{p}^{-1}$