Q 11-09-097JEE MainJEE Main 2023 (8 Apr, Shift 1)Medium
An air bubble of diameter $6$ mm rises steadily through a solution of density $1750\ \text{kg m}^{-3}$ at the rate of $0.35\ \text{cm s}^{-1}$. The coefficient of viscosity of the solution (neglect density of air) is ______ Pa s (given $g=10\ \text{m s}^{-2}$).
Numerical value type. Enter your answer.
Answer: 10
At steady speed the viscous drag balances the upthrust: $6\pi\eta rv=\dfrac43\pi r^3\rho g$.
$$\eta=\frac{2r^2\rho g}{9v}=\frac{2\times9\times10^{-6}\times1750\times10}{9\times0.0035}=10\ \text{Pa s}$$
Solution by Sreeraj P, M.Sc Physics