Question

From the following combinations of physical constants (expressed through their usual symbols) the only combination, that would have the same value in different systems of units, is :

• A. $\frac{ch}{2\pi\epsilon^{2}_{0}}$
• B. $\frac{e^{2}}{2\pi\epsilon_{0}Gm_{e}^{2}}$ ($m_e$ = mass of electron)
• C. $\frac{\mu_{0}\,\epsilon_{0}}{c^{2}} \frac{G}{he^{2}}$
• D. $\frac{2\pi\sqrt{\mu_{0}\epsilon_{0}}}{ce^{2}} \frac{h}{G}$

Answer 1

Answer: (B)

$\frac{e^{2}}{2\pi\epsilon_{0}Gm_{e}^{2}}$ ($m_e$ = mass of electron)

Answer 2

A dimensionless & unitless terms will have
same value is all systems.