Assertion: A dimensionally correct equation may be incorrect.

Reason: Dimensional analysis cannot deduce the dimensionless constants present in the equation

Let $\left[{\in }_0\right]$ denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then :

Stoke's law states that the viscous drag force $F$ experienced by a sphere of radius $a$a, moving with a speed $v$ through a fluid with coefficient of viscosity $\eta$, is given by $F=6\pi \eta av$.

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 values of $a, b$ and $c$ are-