Question

If velocity of light $C$, the gravitational constant $G$ and plank's constant $h$ be chosen as the fundamental units, then find the dimensions of mass, length and time in the new system.

Answer 1

If velocity of light $C$, the gravitational constant $G$ and plank's constant $h$ be chosen as the fundamental units, then the dimensions of mass, length and time in the new system will be $C ^{\frac{1}{2}} h^{\frac{1}{2}} G ^{-\frac{1}{2}} ; C ^{-\frac{3}{2}} h^{\frac{1}{2}} G ^{\frac{1}{2}} ; C ^{-\frac{5}{2}} h^{\frac{1}{2}} G ^{\frac{1}{2}}$