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 pi eta` 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
`(V)/(t)=K ((p)/(l))^(a)eta^(b)r^(c )`
where k is a dimensionless constant. Correct values of a, b and c are -

Options

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`

Answer

A