Stoke's 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 $F=6$ inav. If this fluid is flowing through a cylindrical pipe of radiusr, leng th $/$ and a pressure difference of Pacross its two ends, then the volume of water $V$ which flows through the pipe in time $t$ can be written as $\frac{V}{t}=k\left(\frac{P}{\ell}\right)^{a} \eta^{b} r^{c}$, where $k$ is a dimensional constant. Correct values of $a, b$ and $c$ are

• Correct answer
  A

  $a=1, b=-1, c=4$
• B

  $a=-1, b=1, c=4$
• C

  $a=2, b=-1, c=3$
• D

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

Hence, the correct answer is option: 'A'.