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

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c^{\frac{1}{2}} G^{\frac{1}{2}} h^{\frac{- 1}{2}}

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c^{\frac{1}{2}} G^{\frac{- 1}{2}} h^{\frac{1}{2}}

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c^{\frac{- 1}{2}} G^{\frac{1}{2}} h^{\frac{1}{2}}

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Solution

The correct option is C $c^{\frac{1}{2}} G^{\frac{- 1}{2}} h^{\frac{1}{2}}$
$L e t m \propto c^{x} G^{y} h^{z}$
by substituting the following dimentions :
[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 = $\frac{1}{2}$ ; y= $- \frac{1}{2}$ ,z=+ $\frac{1}{2}$
So m $\propto c^{\frac{1}{2}} G^{\frac{- 1}{2}} h^{\frac{1}{2}}$

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