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?
Answer & explanation
Correct answer: option 1
[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 = \(\frac{\sqrt{hG}}{c^{\frac{3}{2}}}\)