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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$F = M g (1 - \frac{ρ_{0}}{ρ})$

$F = M g (1 + \frac{ρ_{0}}{ρ})$

$F = M g (1 + \frac{ρ}{ρ_{0}})$

$F = M g (1 \pm ρ ρ_{0})$

answer is C.

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Detailed Solution

$\begin{array}{l} F_{V} + F_{b} = M g \\ F_{V} + V ρ_{liquid} g = M g \\ F_{V} = M g - V ρ_{0} g \\ (∵ ρ = \frac{M}{V}) \\ = M g - M g \frac{ρ_{0}}{ρ} \Rightarrow F = M g (1 - \frac{ρ_{0}}{ρ}) \end{array}$

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