If velocity of light (c) , gravitational constant (G) and Planck's constant (h) are chosen as fu

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1.Units, Dimensions and Measurement

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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

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

Solution

(c) 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 $m \propto {c^{1/2}}{G^{ – 1/2}}{h^{1/2}}$

Standard 11

Physics

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