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Question:

Consider two solid spheres P and Q each of density 8 g/cm³ and diameters 1 cm and 0.5 cm respectively. Sphere P is dropped into a liquid of density 0.8 g/cm³ and viscosity η=3 poiseulles. Sphere Q is dropped into a liquid of density 1.6 g/cm³ and viscosity η=2 poiseulles. The ratio of the terminal velocities of P and Q is:

Solution:

Terminal velocity v=2gr²(ρ-σ)/9η

∴ vP/vQ = rP²(ρP-σ1)η2 / rQ²(ρQ-σ2)η1

Given :
η1=3 poise = 30 P
η2=2 poise = 20 P
ρP=ρQ=8 g/cm³
σ1=0.8 g/cm³
σ2=1.6 g/cm³
Radius of sphere P rP=1/2 cm=0.005 m
Radius of sphere Q rQ=0.5/2 cm=0.0025 m

∴ vP/vQ =(0.005)²(8-0.8)(20)/(0.0025)²(8-1.6)(30) = 3