If velocity of light $c$,Planck's constant $h$,and gravitational constant $G$ are taken as fundamental quantities,then express length in terms of dimensions of these quantities.

Given the pressure formula $P = FK$,where $F$ is force,find the dimensional formula of $K$.

The density of a material in $SI$ units is $128 \ kg \ m^{-3}$. In a system of units where the unit of length is $25 \ cm$ and the unit of mass is $50 \ g$,the numerical value of the density of the material is:

Consider the equation $H = \frac{x^p \epsilon^q E^r}{t^s}$, where $H = \text{magnetic field}$, $E = \text{electric field}$, $\epsilon = \text{permittivity}$, $x = \text{distance}$, and $t = \text{time}$. The values of $p, q, r$, and $s$ respectively are:

Obtain the relation between the units of some physical quantity in two different systems of units. Obtain the relation between the $MKS$ and $CGS$ unit of work.

Stokes' law states that the viscous drag force $F$ experienced by a sphere of radius $a$,moving with a speed $v$ through a fluid with coefficient of viscosity $\eta$,is given by $F=6 \pi \eta a v$. If this fluid is flowing through a cylindrical pipe of radius $r$,length $l$ and pressure difference of $p$ across its two ends,then the volume of water $V$ which flows through the pipe in time $t$ can be written as $\frac{V}{t}=k\left(\frac{p}{l}\right)^a \eta^b r^c$,where $k$ is a dimensionless constant. Correct values of $a, b$ and $c$ are