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

\(\frac{\sqrt{hG}}{c^{\frac{3}{2}}}\) \(\frac{\sqrt{hG}}{c^{\frac{5}{2}}}\) \(\sqrt{\frac{hc}{G}}\) \(\sqrt{\frac{Gc}{h^{\frac{3}{2}}}}\)

\(\frac{\sqrt{hG}}{c^{\frac{3}{2}}}\)

[L] = [hacbGc] [L] = [ML2T-1]a[LT-1]b[M-1L3T-2]c On solving : a = 1/2 ; b = -3/2 ; c = 1/2 L = \(\frac{\sqrt{hG}}{c^{\frac{3}{2}}}\)