An air bubble of radius R is rising in a liquid of density and viscosity . A solid spherical ball of the same radius R and density 3 is falling in the same liquid. Neglecting the density of air, what is the ratio of the terminal speed of the air bubble to that of the solid ball?

Step-by-step solution

The terminal velocity v of a spherical object of radius r and density moving in a liquid of density and viscosity is given by: v = 2r^2g 9 | - | For the rising air bubble, the density of air is negligible ( 0 ). The effective density difference driving the motion is |0 - | = . Thus, its terminal speed is: v₁ = 2R^2g 9 For the falling solid ball, its density is = 3 . The effective density difference is |3 - | = 2 . Thus, its terminal speed is: v₂ = 2R^2g(2 ) 9 The ratio of their terminal speeds is: v₁ v₂ = 2 = 1 2 T