If the capacitance of a nanocapacitor is measured in terms of a unit $u$ made by combining the electric charge $e,$ Bohr radius $a_0,$ Planck's constant $h$ and speed of light $c$ then
$u\, = \,\frac{{{e^2}h}}{{{a_0}}}$
$u\, = \,\frac{{hc}}{{{e^2}{a_0}}}$
$u\, = \,\frac{{{e^2}c}}{{h{a_0}}}$
$u\, = \,\frac{{{e^2}{a_0}}}{{hc}}$
The dimension of $P = \frac{{{B^2}{l^2}}}{m}$ is
where $B=$ magnetic field, $l=$ length, $m =$ mass
Whose dimensions is $M{L^2}{T^{ - 1}}$
The dimension of $\frac{1}{2} \varepsilon_0 E ^2$, where $\varepsilon_0$ is permittivity of free space and $E$ is electric field, is
The dimensions of universal gravitational constant are
In the expression $P = El^2m^{-5}G^{-2}$, $E$, $l$, $m$ and $G$ denote energy, mass, angular momentum and gravitational constant respectively. Show that $P$ is a dimensionless quantity.