Question

A soap bubble of radius \(r = 1\,\text{mm}\) is rising in a liquid of density \( \rho = 2000\,\text{kg/m}^3 \). At the instant the bubble is rising upward with constant velocity \(v = \tfrac{1}{2}\,\text{cm/s}\). Find the coefficient of viscosity \( (\eta) \).

• A. \( \dfrac{2}{9}\ \text{N·s/m}^2 \)
• B. \( \dfrac{4}{9}\ \text{N·s/m}^2 \)
• C. \( \dfrac{2}{3}\ \text{N·s/m}^2 \)
• D. \( \dfrac{8}{9}\ \text{N·s/m}^2 \)

Hint:

For terminal velocity problems using Stokes' law: \[ v = \frac{2r^2(\rho-\rho_f)g}{9\eta} \] For bubbles, density of gas is negligible, so \( \rho_f \) dominates.

Answer 1

The Correct Option is A