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

Options

A. `C^0 g P^(-3)`
B. `C^2 g^3 P^(-2)`
C. `C^(0) g^2 P^(-1)`
D. `C^2 g^2 P^(-2)`

Answer

C

Explanation

Let `G = C^x g^y Pz`
`[M^(-1) L^(-3)T^(-2)] = [LT^(-1)]^x [LT^(-2)]^y [ML^(-1)T^(-2)]^z`
`= M^(z) L^(x + y - z) T^(-x - 2y - 2z)`
Applying principle of homogencity of dimensions, we get
`z = -1 , x + y - z = 3`
`-x - 2y - 2z = -2`
On solving , we get
`y = 2, x = 0`
`therefore G = C^0 g^2 P^(-1)`