A small ball of mass M and density ρ is dropped in a viscous liquid of density ρ₀. After some time, the ball falls with a constant velocity. What is the viscous force on the ball?
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Question

A small ball of mass M and density ρ is dropped in a viscous liquid of density ρ₀. After some time, the ball falls with a constant velocity. What is the viscous force on the ball?

G1 Physics · Accepted Answer

At terminal velocity, the net force on the ball is zero. Downward force = Mg Upward forces: 1. Buoyant force = ρ₀Vg 2. Viscous force = F Therefore, Mg = F + ρ₀Vg Since M = ρV, we have V = M/ρ. So, F = Mg - ρ₀(M/ρ)g = Mg(1 - ρ₀/ρ) Hence option C follows.