If C the velocity of light,h Planck's constant and G gravitational constant are taken as fundamental quantities, then the dimensional formula of mass is

Options

A. `h^(-1//2)G^(1//2)C^(0)`
B. `h^(1//2)C^(1//2)G^(-1//2)`
C. `h^(-1//2)C^(1//2)G^(-1//2)`
D. `h^(-1//2)C^(-1//2)G^(-1//2)`

Answer

B

Explanation

`M = C^(a)h^(b)G^(c )`
The dimensional formula of above expression is given as,
`[ML^(0)T^(0)] = [LT^(-1)]^(a) [ML^(2)T^(-1)]^(b) [M^(-1)L^(3)T^(-2)]^(c )`
`[M]^(1) = M^(b-c) implies b - c = 1` …(1)
` L^(0) = L^(a+2b+3c) implies a+2b+3c = 0 ` ...(2)
`T^(0) = T^(a-b-2c) implies a+b+2c = 0` ...(3)
On solving equations (1),(2)and (3), we get,
`a=1/2, b=1/2, c=1/2`
`:. M = h^(1//2)C^(1//2)G^(-1//2)`