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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.

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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)

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