Question

A solid ball of density ρ₁ and radius r falls vertically through a liquid of density ρ₂. Assume that the viscous force acting on the ball is F = krv, where k is a constant and v its velocity. What is the terminal velocity of the ball?

Options

• `(4pir^2(rho_1 - rho_2))/(3k)`

• `(2pir(rho_1 - rho_2))/(3gk)`

• `(2pig(rho_1 + rho_2))/(3gr^2k)`

• None of these

Answer 1

`bb((4pir^2(rho_1 - rho_2))/(3k))`

Explanation:

The Net force on the ball = 0.

(when terminal velocity is attained).

Hence,

Weight = upthrust + viscous force

∴ `4/3pir^3rho_1g = 4/3pir^3rho_2g + krv_r`

∴ `v_T = (4pigr^2)/(3k)(rho_1 - rho_2)`