If an air bubble of diameter 2 mm rises steadily through a liquid of density 2000 kg/m ^3 at a rate of 0.5 cm/s, then the coefficient of viscosity of liquid is _______ Poise. (Take g = 10 m/s ^2 )

Step-by-step solution

The terminal velocity of an air bubble rising in a liquid is given by Stokes' law: v = 2 9 r^2 g Where: r = D 2 = 1 mm = 10⁻³ m = 2000 kg/m ^3 g = 10 m/s ^2 v = 0.5 cm/s = 5 10⁻³ m/s Rearranging the formula for the coefficient of viscosity : = 2 9 r^2 g v Substituting the given values: = 2 9 (10⁻³)^2 2000 10 5 10⁻³ = 2 9 10⁻⁶ 20000 5 10⁻³ = 2 9 2 10⁻² 5 10⁻³ = 2 9 4 = 8 9 Pa s To convert the viscosity from SI units (Pa s) to CGS units (Poise), we multiply by 10 : = 8 9 10 = 80 9 Poise 8.88 Poise The closest given o