Plancks constant (h), speed of light in vacuum (c) and Newtons gravitational constant (G) are three fundamental constants. Which of the following combinations of these has dimension of length?
$\sqrt{\dfrac{Gc}{h^{3/2}}}$
$\dfrac{\sqrt{hG}}{c^{3/2}}$
$\dfrac{\sqrt{hG}}{c^{5/2}}$
$\sqrt{\dfrac{hc}{G}}$
Explanation:
L = (h)a (c)b (G)c
m0L1T0 = (m1L2T–1)a (L1T–1)b (m–1C3T–2) c
a – c = 0, 2a + b + 3c = 1, – a – b –2c = 0
solving b = –3/2, a = 1/2, c = 1/2
L = $\dfrac{\sqrt{hG}}{c^{3/2}}$