Question

If the velocity of light $c$, gravitational constant $G$ and Planck's constant $h$ be taken as fundamental units the dimension of mass in the new system will be

• A. $c^{1/2}{h}^{1/2}{G}^{1/2}$
• B. $c^{1/2}{h}^{1/2}{G}^{-1/2}$
• C. $c^{-3/2}{h}^{1/2}{G}^{1/2}$
• D. $c^{-5/2}{h}^{1/2}{G}^{1/2}$

Answer 1

Answer: (B)

$c^{1/2}{h}^{1/2}{G}^{-1/2}$

$C\equiv L{T}^{-1}$

$G\equiv M^{-1}{L}^3{T}^{-2}$

$h\equiv M^1{L}^2{T}^{-1}$

$\Rightarrow M=\sqrt{\frac{hc}{G}}$