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
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
${c^{1/2}}{G^{1/2}}{h^{1/2}}$
${c^{1/2}}{G^{1/2}}{h^{ - 1/2}}$
${c^{1/2}}{G^{ - 1/2}}{h^{1/2}}$
${c^{ - 1/2}}{G^{1/2}}{h^{1/2}}$
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
Let $m \propto {C^x}{G^y}{h^z}$
By substituting the following dimensions :
$[C] = L{T^{ - 1}};\,[G] = [{M^{ - 1}}{L^3}{T^{ - 2}}]$ and $[h] = [M{L^2}{T^{ - 1}}]$
Now comparing both sides we will get
$x = 1/2;\,y = - 1/2,\,z = + 1/2$
So $m \propto {c^{1/2}}{G^{ - 1/2}}{h^{1/2}}$
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