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Question:

Neglecting the density of air, the terminal velocity obtained by a raindrop of radius 0.3 mm falling through air of viscosity 1.8×10⁻⁵ Nsm⁻² will be:

7.48 ms⁻¹;

12.8 ms⁻¹;

10.9 ms⁻¹;

3.7 ms⁻¹;

Solution:

Neglecting the density of air, and hence buoyant force due to air, at equilibrium, 4/3ρπr³g = 6πηrv ⇒ v = 2r²g/9ηρ = 2 × 0.0003² × 1000 × 9.8 / (9 × 1.8 × 10⁻⁵) m/s = 10.9 m/s