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 p^z`
`[M^(-1)L^3 T^(-2)] = (LT^(-1 ^(x))) (LT^(-2))^y (ML^(-1) T^(-2))^z`
`=M^z L^(x+y) T^(-x-2y-2z)`
Applying principle of homogeneity of dimensions, we get
z = 1, x+y - x=3.
-x -2y -2z = -2
On solving, we get, y= 2, z=0
`:. G = c^0 g^2 p^(-1)`