A solid ball of density ρ 1 and radius r falls vertically through a liquid of density ρ 2 . Assume that the viscous force acting on the ball is F = k r v , where k is a constant and v its velocity. What is the terminal velocity of the ball?

Question

A solid ball of density ρ 1 and radius r falls vertically through a liquid of density ρ 2 . Assume that the viscous force acting on the ball is F = k r v , where k is a constant and v its velocity. What is the terminal velocity of the ball?, 4 π g r 2 ρ 1 - ρ 2 3 k, 2 π r ρ 1 - ρ 2 3 g k, 2 π g ρ 1 + ρ 2 3 g r 2 k, none of these

MARKS App · Accepted Answer

Net force on the ball = 0 (when terminal velocity is attained). Hence, Weight=upthrust+viscous force ∴ 4 3 π r 3 ρ 1 g = 4 3 π r 3 ρ 2 g + k rv T ∴ v T = 4 π g r 2 3 k ρ 1 - ρ 2

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