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Question

If the velocity of light $\mathrm{c}$, universal gravitational constant $\mathrm{G}$ and Planck's constant $\mathrm{h}$ are chosen as fundamental quantities. The dimensions of mass in the new system is :

$\left[\mathrm{h}^{1} \mathrm{c}^{1} \mathrm{G}^{-1}\right]$
$\left[\mathrm{h}^{-1 / 2} \mathrm{c}^{1 / 2} \mathrm{G}^{1 / 2}\right]$
$\left[\mathrm{h}^{1 / 2} \mathrm{c}^{1 / 2} \mathrm{G}^{-1 / 2}\right]$
$\left[\mathrm{h}^{1 / 2} \mathrm{c}^{-1 / 2} \mathrm{G}^{1}\right]$

Solution

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