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Two small spherical metal balls, having equal masses, are made from materials of densities ρ₁ and ρ₂ (ρ₁ = 8ρ₂) and have radii of 1 mm and 2 mm, respectively. They are made to fall vertically (from rest) in a viscous medium whose coefficient of viscosity equals η and whose density is 0.1ρ₂. The ratio of their terminal velocities would be:

1. 79 / 36
2. 89 / 72
3. 19 / 36
4. 39 / 72

Correct answer: 79 / 36

Solution

The terminal velocity of a sphere in a viscous medium is proportional to the square of its radius and the difference in density between the sphere and the medium. Using the given densities and radii, the ratio of terminal velocities is calculated as (r₁²(ρ₁ - ρ_medium)) / (r₂²(ρ₂ - ρ_medium)) = 79/36.

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