If electronic charge $e$, electron mass $m$, speed of light in vacuum $c$ and Planck 's constant $h$ are taken as fundamental quantities, the permeability of vacuum $\mu _0$ can be expressed in units of
$\left( {\frac{h}{{m{e^2}}}} \right)$
$\left( {\frac{{hc}}{{m{e^2}}}} \right)$
$\left( {\frac{h}{{c{e^2}}}} \right)$
$\left( {\frac{{m{c^2}}}{{h{e^2}}}} \right)$
If the constant of gravitation $(G)$, Planck's constant $(h)$ and the velocity of light $(c)$ be chosen as fundamental units. The dimension of the radius of gyration is
A dimensionally consistent relation for the volume V of a liquid of coefficient of viscosity ' $\eta$ ' flowing per second, through a tube of radius $r$ and length / and having a pressure difference $P$ across its ends, is
In the equation $y = pq$ $tan\,(qt)$, $y$ represents position, $p$ and $q$ are unknown physical quantities and $t$ is time. Dimensional formula of $p$ is
If velocity of light $c$, Planck’s constant $h$ and gravitational constant $G$ are taken as fundamental quantities, then express time in terms of dimensions of these quantities.
Even if a physical quantity depends upon three quantities, out of which two are dimensionally same, then the formula cannot be derived by the method of dimensions. This statement