Question

A gas bubble of 2 cm diameter rises through a liquid of density 1.75 gm $c{m}^{-3}$ with a fixed speed of 0.35 cm $s^{-1}$. Neglect the density of the gas. The coefficient of viscosity of the liquid is:

• A. 870 poise
• B. 1120 poise
• C. 982 poise
• D. 1089 poise

Answer 1

Answer: (D)

1089 poise

As gas bubble is moving upward with constant speed so Buoyant force = Viscous drag force
$\Rightarrow F_b=F_v\Rightarrow \left(\frac{4}{3}\pi r^3\right)\rho g=6\pi \eta rv$

$\Rightarrow \eta =\frac{2}{9}\frac{r^2\rho g}{v}$

Here, $r=1cm,$

$\rho =1.75gc{m}^{-3},$
$g=980cm{s}^{-2}$
$v=0.35cm{s}^{-1},$

$\eta =$?
$\therefore \eta =\frac{2}{9}\times \frac{1^2\times 1.75\times 980}{0.35}$

$=1088.88\approx 1089poise$