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

Options

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

Answer

A

Explanation

` h = [ ML^(2) T^(-1)] , G = [M^(1) L^(3) T^(-2)] , C = [LT^(-1)]`
`:. h^(1//2) G^(-1//2) C^(1//2) = M^(1//2) L T^(-1//2) xx M^(1//2) L^(-3//2) xx L^(1//2) T^(-1//2)`
`= ML^(0)T^(0) = Mass`