Stoke's law states that the viscous drag force $F$ experience by a sphere of radius a, moving with a speed $\mathrm{v}$ through a fluid with coefficient of viscosity $\eta$, is given by $F=6 \pi n a v$ If this fluid is flowing through a cylindrical pipe of radius $\mathrm{r}$, length 1 and a pressure difference of P across its two ends, then the volume of water $\mathrm{V}$ which flows through the pipe in time $\mathrm{t}$ can be written as $$ \frac{v}{t}=k\left(\frac{p}{l}\right)^{a} \eta^{b} r^{c} $$ Where $\mathrm{k}$ is a dimensionless constant. Correct values of $\mathrm{a}, \mathrm{b}$ and $\mathrm{c}$ are

• Correct answer
  A

  $\mathrm{a}=1, \mathrm{~b}=-1, \mathrm{c}=4$
• B

  $\mathrm{a}=-1, \mathrm{~b}=1, \mathrm{c}=4$
• C

  $\mathrm{a}=2, \mathrm{~b}=-1, \mathrm{c}=3$
• D

  $\mathrm{a}=1, \mathrm{~b}=-2, \mathrm{c}=-4$

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