The expression $[M{L^2}{T^{ - 2}}]$ represents

The electrical resistance $R$ of a conductor of length $l$ and area of cross section $a$ is given by $R = \frac{{\rho l}}{a}$ where $\rho$ is the electrical resistivity. What a is the dimensional formula for electrical conductivity $\sigma $ which is reciprocal of resistivity?

A quantity $x$ is given by $\left( IF v^{2} / WL ^{4}\right)$ in terms of moment of inertia $I,$ force $F$, velocity $v$, work $W$ and Length $L$. The dimensional formula for $x$ is same as that of

Which of the following quantities have dimensions of $\frac{{\pi {{\Pr }^4}}}{{3Ql}}:$ ( $Q =$ Volume flow rate in $m^3/s$ and $P =$ pressure)

The dimensions of resistivity in terms of $M,\,L,\,T$ and $Q$ where $Q$ stands for the dimensions of charge, is

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 a 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 value of $a, b$ and $c$ are