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.

Explanation

`C = [LT^(-1)] rarr (1), h = [ML^(2) T^(-1)] rarr (2)`
`G = [M^(-1) L^(3) T^(-2)] rarr (3)`
Solving (2) and (3)
`(h)/(G) = [(ML^(2)T^(-1))/(M^(-1) L^(3) T^(-2))] = [M^(2) L^(-1) T^(1)]`
Substituing (1) in above
`(h)/(G) = (M^(2))/(C) implies [M] = [h^(1/2) G^(-1/2) C^(1/2)]`