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.

The volume of a liquid flowing out per second of a pipe of length $l$ and radius $r$ is written by a student as $V = \frac{\pi p r^4}{8 \eta l}$,where $p$ is the pressure difference between the two ends of the pipe and $\eta$ is the coefficient of viscosity of the liquid having the dimensional formula $[M^1 L^{-1} T^{-1}]$. Check whether the equation is dimensionally correct.

If the charge of electron $e$,mass of electron $m$,speed of light in vacuum $c$,and Planck's constant $h$ are taken as fundamental quantities,then the permeability of vacuum $\mu_0$ can be expressed as

$E, m, L, G$ represent energy,mass,angular momentum,and gravitational constant respectively. The dimensions of $\frac{EL^2}{m^5 G^2}$ will be that of

$E, m, l$ and $G$ denote energy,mass,angular momentum,and gravitational constant respectively. Then the dimensions of $\frac{El^2}{m^5G^2}$ are:

Velocity $(v)$ and acceleration $(a)$ in two systems of units $1$ and $2$ are related as $v_{2} = \frac{n}{m^{2}} v_{1}$ and $a_{2} = \frac{a_{1}}{mn}$ respectively. Here $m$ and $n$ are constants. The relations for distance $(L)$ and time $(T)$ in the two systems are: