Question

A small ball of mass 'm' and density ρ is dropped in a viscous liquid of density ρ₀. After sometime the ball falls with constant velocity. Calculate the viscous force acting on the ball.

Answer 1

Volume of the ball(V) = m/ρ

Mass of the liquid displaced by the ball,

m' = (m/ρ)ρ₀

When the ball falls with a constant velocity, then,

Viscous force = effective weight of the ball

or F = mg - m'g = (m - m')g

= (m -(mρ⁰/ρ))g = mg(1 - ρ₀/ρ)