A physical quantity of the dimensions of length that can be formed out of $c, G$ and $\frac{e^2}{4\pi \varepsilon _0}$ is $[c$ is velocity of light, $G$ is the universal constant of gravitation and $e$ is charge $] $
$\frac{1}{{{c^2}}}$$\sqrt {\frac{{{e^2}}}{{G4\pi \varepsilon_0}}} $
$\frac{1}{{{c^{}}}}\frac{{G{e^2}}}{{4\pi \varepsilon_0}}$
$\frac{1}{{{c^2}}}$$\sqrt {\frac{{G{e^2}}}{{4\pi \varepsilon_0}}} $
${c^2}\;\sqrt {\frac{{G{e^2}}}{{4\pi \varepsilon_0}}} $
If $R , X _{ L }$. and $X _{ C }$ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless:
Force $F$ is given in terms of time $t$ and distance $x$ by $F = a\, sin\, ct + b\, cos\, dx$, then the dimension of $a/b$ is
If the dimensions of length are expressed as ${G^x}{c^y}{h^z}$; where $G,\,c$ and $h$ are the universal gravitational constant, speed of light and Planck's constant respectively, then
The physical quantity which has dimensional formula as that of $\frac{{{\rm{Energy}}}}{{{\rm{Mass}} \times {\rm{Length}}}}$ is
convert $1\; newton$ ($SI$ unit of force) into $dyne$ ($CGS$ unit of force)