alleryTerminal velocity of sphere (radius r, density ρ_s) falling in viscous fluid (density ρ_f, viscosity η):
Av_t = ρgh
Bv_t = g × r
Cv_t = (2/9) × (ρ_s - ρ_f) g r² / η
Dv_t = mg
Answer & Solution
Correct answer: C. v_t = (2/9) × (ρ_s - ρ_f) g r² / η
**At terminal velocity:** weight - buoyancy = drag.
(4/3)πr³(ρ_s - ρ_f)g = 6πηr × v_t.
**Solve:** v_t = (2/9)(ρ_s - ρ_f) g r²/η. v_t ∝ r².
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