Question

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^1/2G^1/2h^1/2
• B. c^1/2G^1/2h^-1/2
• C. c^1/2G^-1/2h^1/2
• D. c^-1/2G^1/2h^1/2

Answer 1

The correct option is C c^1/2G^-1/2h^1/2

$Letm\propto c^x{G}^y{h}^z$
by substituting the following dimentions :
[c] = $L{T}^{-1}$; [G] = $\left[M^{-1}{L}^3{T}^{-2}\right]$ and [h] = $\left[M{L}^2{T}^{-1}\right]$
Now comparing both sides we will get
x = $\frac{1}{2}$; y=$-\frac{1}{2}$,z=+$\frac{1}{2}$
So m$\propto c^{\frac{1}{2}}{G}^{\frac{-1}{2}}{h}^{\frac{1}{2}}$