Physics

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


ANSWER

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


SOLUTION

$$C\equiv LT^{-1}$$

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

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

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

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