Q 11-09-037JEE MainJEE Main 2026 (2 Apr, Shift 2)Medium
If an air bubble of diameter $2$ mm rises steadily through a liquid of density $2000\ \text{kg/m}^3$ at a rate of $0.5$ cm/s, then the coefficient of viscosity of liquid is ______ Poise. (Take $g=10\ \text{m/s}^2$)
Answer: (B) $8.8$
At terminal speed, buoyancy minus the (negligible) weight of air equals Stokes' drag:
$$6\pi\eta rv=\frac43\pi r^3\rho g\ \Rightarrow\ \eta=\frac{2r^2\rho g}{9v}$$
$\eta=\dfrac{2\times(10^{-3})^2\times2000\times10}{9\times0.005}=\dfrac{0.04}{0.045}\approx0.89$ Pa s
Since $1$ Pa s $=10$ poise, $\eta\approx8.9$ poise, i.e. about $8.8$ poise.
Solution by Sreeraj P, M.Sc Physics