A liquid of density `rho=1000kg//m^(3)` viscosity `eta=0.1 Ns//m^(2)` is flowing down in vertical pipe of large cross section. A small ball of density `rho_(0)=100 kg//m^(3)` and `r=5cm` will be at rest in flowing liquid, if velocity of flowing liquid is `10 k m//s`. Then find the value of `k`.

Explanation

In fluid frame ball is moving with constant velocity (terminal) and resultant of all forces acting on it zero.
(`A`) Buoyant force (`B`) Viscous force (`C`) `mg`
`v_(1)=(2)/(9)((rho-rho_(0))gr^(2))/(eta)=(2)/(9)xx(900xx10)/(0.1)xx25xx10^(-4)=50m//s`