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Two solid spheres P and Q, each of density 8 g/cm³, have diameters of 1 cm and 0.5 cm respectively. Sphere P falls through a liquid of density 0.8 g/cm³ and viscosity 3 poise, while sphere Q falls through a different liquid of density 1.6 g/cm³ and viscosity 2 poise. What is the ratio of the terminal velocity of P to that of Q?
- 3: 1
- 3: 4
- 3: 2
- 3: 8
Correct answer: 3: 1
Solution
Using Stokes' law, v_T is proportional to r²*(rhoₛ - rhoₗ)/eta. For P: r=0.5 cm, effective density difference=7.2 g/cm³, eta=3 poise; for Q: r=0.25 cm, difference=6.4 g/cm³, eta=2 poise. The ratio works out to 3:1.
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