Question

An air bubble of diameter 2mm rises steadily througha solution of density $1750kg/m^3$at the rate of $0.35cm/s$.Calculate the coefficient of viscosity of the solution.The density of air is negligible.

• A. 10
  
• B. 11
• C. 12
  
• D. 13

Answer 1

The correct option is B 11

The force of buoyancy B is equal to the weight of the displaced liquid. Thus

$\Rightarrow B=\frac{4}{3}\pi r^{3}6g$

This force is upward. The viscous force acting downward is $F=6\pi nrv$

The weight of the air bubble may be neglected as the density of air is small. for uniform velocity -

$\Rightarrow F=B$

$\Rightarrow 6\pi nrv=\frac{4}{3}\pi r^{3}6g$

$\Rightarrow n=\frac{2r^{3}6g}{9v}$

$=\frac{2\times {(1\times 106-3m)}^2\times \left(1750kg/m^3\right)\times 9.8m/s^2}{9\times 0.35\times {10}^{-2}m/s}$

$=11poise$

This appears to be a highly viscous liquid.