alleryThe condition for **terminal velocity** of a sphere falling in a viscous fluid is that:
AViscous force exceeds gravity
BNet force is zero: weight = viscous drag + buoyant force
CThe fluid is at rest
DGravity is zero
Answer & Solution
Correct answer: B. Net force is zero: weight = viscous drag + buoyant force
At terminal velocity, sphere falls at constant speed: net force = 0. $mg = 6\pi\eta r v_t + (4/3)\pi r^3 \sigma g$ (sphere weight = viscous drag + upthrust).
Solving gives $v_t = (2/9)r^2(\rho - \sigma)g/\eta$.
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