If speed of light (c), acceleration due to gravity (g) and pressure (P) are taken as fundamental units, the dimensions of gravitational constant (G) are

If speed of light (c), acceleration due to gravity (g) and pressure (P

1.	If speed of light (c), acceleration due to gravity (g) and pressure (P) are taken as fundamental units, the dimensions of gravitational constant (G) are
Answer» `[c^(0)gP^(-3)]` `[c^(2)g^(3)P^(-2)]` `c^(0)g^(2)P^(-1)]` `c^(2)g^(2)P^(-2)]` SOLUTION :Let`G= kc^(x)g^(y)P^(z)` Where k is a dimensionless constant. `:. [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 HOMOGENEITY of dimensions we get, z=- 1...(i) x+y-z= 3...(ii) -x-2y-2z= -2,..(iii) On solving (i), (ii) and (iii) we get, `x=0, y=2, z=-1 :. [G]= [c^(0)g^(2)P^(-1)]`