Q. A physical quantity of the dimensions of length that can be formed out of c, G and $\frac{e^2}{4\pi\epsilon_0}$ is [c is velocity of light, G is universal constant of gravitation and e is charge] :
A) $\frac{1}{c^2}\left[G\frac{e^2}{4\pi\epsilon_0}\right]^{1/2}$
B) $c^2\left[G\frac{e^2}{4\pi\epsilon_0}\right]^{1/2}$
C) $\frac{1}{c^2}\left[\frac{e^2}{G4\pi\epsilon_0}\right]^{1/2}$
D) $\frac{1}{c}G\frac{e^2}{4\pi\epsilon_0}$
Explanation
[Solution] $[e^2/4\pi\epsilon_0] = [ML^3T^{-2}]$, $[G] = [M^{-1}L^3T^{-2}]$; $[G e^2/4\pi\epsilon_0]^{1/2} = [L^3T^{-2}]$, and dividing by $c^2$ ($[L^2T^{-2}]$) gives [L]. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.