If the velocity of light `(c)` , gravitational constant `(G)` and Planck's constant `(h)` are chosen as fundamental units, then the dimensions of mass in new system is

Options

A. `c^(1//2) G^(1//2) h^(1//2) `
B. `c^(1//2) G^(1//2) h^(-1//2) `
C. `c^(1//2) G^(-1//2) h^(1//2) `
D. `c^(-1//2) G^(1//2) h^(1//2) `

Answer

C

Explanation

`mprop C^(a)G^(b)h^(c) implies m prop C^(1//2)G^(-1//2)h^(1//2)`
`[M]=[LT^(-1)]^(a) [M^(-1)L^3T^(-2)][ML^2T^(-1)]^c`
`=[M^(-b+c)L^(a+3b+2c)T^(-a-2b-c)]`
`-b+c=1`
`a +3b +2c =0`
`-a -2b -c =0`
By equation (ii) and (iii)
`b+c=0`
By equation (iv) and (i)
`c=1/2 , b =-1/2`
From equation (iii) `-a+1 -1/2 = 0 implies a =1/2`