If velocity of light C, universal gravitational constant G and Planck's constant h are fundamental quantities in a system of measurements, then the dimensional formula for mass is

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$C^{\frac{1}{2}} G^{\frac{3}{2}} h^{\frac{1}{2}}$

$C^{\frac{1}{2}} G^{\frac{- 1}{2}} h^{\frac{1}{2}}$

$C^{\frac{3}{2}} G^{\frac{- 1}{2}} h^{\frac{1}{2}}$

$C^{\frac{1}{2}} G^{\frac{1}{2}} h^{\frac{1}{2}}$

answer is A.

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Detailed Solution

$\begin{array}{l} M \propto h^{x} e^{y} G^{z} \\ M \propto {(M L^{2} T^{- 1})}^{x} {(L T^{- 1})}^{y} {(M^{- 1} L^{3} T^{- 2})}^{z} \\ \to M = h^{1 / 2} C^{1 / 2} G^{- 1 / 2} \end{array}$

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