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Planck’s constant (h), speed of light in vacuum (c) and Newton’s gravitational constant (G) are three fundamental constants. Which of the following combination of these has the dimension of length ?

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$\sqrt{\frac{h c}{G}}$

$\sqrt{\frac{G c}{h^{3 / 2}}}$

$\sqrt{\frac{h G}{c^{5 / 2}}}$

$\frac{\sqrt{h G}}{c^{3 / 2}}$

answer is A.

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Detailed Solution

$\frac{\sqrt{h G}}{C^{3 / 2}} = \frac{\sqrt{M L^{2} T^{- 1} M^{- 1} L^{3} T^{- 2}}}{{(L T^{- 1})}^{3 / 2}}$

$= \frac{L^{5 / 2} T^{- 3 / 2}}{L^{3 / 2} T^{- 3 / 2}} = L$

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