Question

A physical quantity of the dimensions of mass that can be formed out of $c$, $G$ and $\frac{e^2}{8\pi {\epsilon }_0}$ is $c$ is velocity of light, $G$ is universal constant of gravitation and $e$ is charge, ${\epsilon }_0$ is electrical permittivity ):

• A. $c{\left[G\frac{e^2}{8\pi {\epsilon }_0}\right]}^{\frac{1}{2}}$
• B. $c^0{\left[\frac{G{e}^2}{8\pi {\epsilon }_0}\right]}^2$
• C. $c{\left[\frac{e^2}{G8\pi {\epsilon }_0}\right]}^{\frac{1}{2}}$
• D. $c^0{\left[\frac{G{e}^2}{8\pi {\epsilon }_0}\right]}^{\frac{1}{2}}$

Answer 1

Answer: (B)

$c^0{\left[\frac{G{e}^2}{8\pi {\epsilon }_0}\right]}^2$

According to question

$c=L{T}^{-1}$
$a=L^3{T}^{-2}{M}^{-1}$
$e=TA$
${\in }_0=L^{-3}{T}^4{A}^2{M}^{-1}$
Now, $\frac{1}{C^2}{\left[G\frac{e^2}{4x{\in }_0}\right]}^{1/2}=\frac{1}{L^{2}T-2}\times \left(L^6{T}^{-4}\right)\times (L^6{T}^{-4}{)}^{1/2}$
$=L$