Q. 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
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) $c^{- 1/2}G^{1/2}h^{1/2}$
Explanation
Let $m \propto C^{x}G^{y}h^{z}$ By substituting the following dimensions: $\lbrack C\rbrack = LT^{- 1};\lbrack G\rbrack = \lbrack M^{- 1}L^{3}T^{- 2}\rbrack$ and $\lbrack h\rbrack = \lbrack ML^{2}T^{- 1}\rbrack$ Now comparing both sides we will get $x = 1/2;y = - 1/2,\ z = \ + 1/2$ So $m \propto c^{1/2}G^{- 1/2}h^{1/2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.