In terms of basic units of mass $(M)$, length $(L)$, time $(T)$ and charge $(Q)$, the dimensions of magnetic permeability of vacuum $\left(\mu_0\right)$ would be
$\left[ MLQ ^{-2}\right]$
$\left[ LT ^{-1} Q ^{-1}\right]$
$\left[ ML ^2 T ^{-1} Q ^{-2}\right]$
$\left[ LTQ ^{-1}\right]$
What is Dimensional Analysis ? State uses of Dimensional Analysis.
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.
The equation of state of some gases can be expressed as $\left( {P + \frac{a}{{{V^2}}}} \right) = \frac{{b\theta }}{l}$ Where $P$ is the pressure, $V$ the volume, $\theta $ the absolute temperature and $a$ and $b$ are constants. The dimensional formula of $a$ is