Question

A solid ball of density r₁ and radius r falls vertically through a liquid of density r₂. Assume that the viscous force acting on the ball is F = krn, where k is a constant and n its velocity. What is the terminal velocity of the ball ?

• A. $\frac{4\pi r^{2}(\rho_{1}–\rho_{2})}{3k}$
• B.
• C. $\frac{2\pi g(\rho_{1} + \rho_{2})}{3gr^{2}k}$
• D. None of these

Answer 1

Answer: (A)

$\frac{4\pi r^{2}(\rho_{1}–\rho_{2})}{3k}$

Answer 2

Net force on the ball = 0

(when terminal velocity is attained).

Hence,

Weight = upthrust + viscous force

\ $\frac{4}{3}$ pr³ r₁g = $\frac{4}{3}$ pr³r₂g + krn_T

\ n_T = $\frac{4\pi gr^{2}}{3k}$ (r₁ – r₂)