Question

An air bubble of radius $1.0cm$ rises with a constant speed of $3.5mm/s$ through a liquid of density $1.75\times {10}^{3}kg/m^3$. The coefficient of viscosity of the liquid is: (Neglect the density of air)

• A. $109Ns/m^2$
• B. $10.9Ns/m^2$
• C. $1.09Ns/m^2$
• D. $0.109Ns/m^2$

Answer 1

Answer: (A)

$109Ns/m^2$

Given,
Terminal velocity$=3.5mm/s$
$\frac{2r^2\left(\rho \right)g}{9\eta }=3.5mm/s$
$\frac{2\times {10}^{-4}\times 1.75\times {10}^3\times 9.8}{9\eta }=3.5\times {10}^{-3}m/s$
$\eta =\frac{2\times 1.75\times {10}^2\times 9.8}{9\times 3.5}Ns/m^2$
$\eta =108.88Ns/m^2$
$\eta \approx 109Ns/m^2$