Q. 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?
A) $\frac{\sqrt{hG}}{c^{3/2}}$
B) $\frac{\sqrt{hG}}{c^{5/2}}$
C) $\sqrt{\frac{hc}{G}}$
D) $\sqrt{\frac{Gc}{h^{3/2}}}$
Explanation
[Solution] Setting $L = h^ac^bG^c$ and solving the dimensions gives a = c = 1/2, b = -3/2: $\sqrt{hG}/c^{3/2}$ (the Planck length). Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.