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

• A

  $a=1, b=-1, c=4$

• B

  $a=-1, b=1, c=4$

• C

  $a=2, b=-1, c=3$

• D

  $a=1, b=-2, c=-4$