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Question 8

A small ball of mass $$m$$ and density $$\rho$$ is dropped in a viscous liquid of density $$\rho_0$$. After sometime, the ball falls with constant velocity. The viscous force on the ball is :

At terminal velocity: Weight = Buoyant force + Viscous force.

$$mg = \frac{m\rho_0}{\rho}g + F_v$$ (buoyant force = $$V\rho_0 g = \frac{m}{\rho}\rho_0 g$$).

$$F_v = mg - \frac{m\rho_0 g}{\rho} = mg\left(1 - \frac{\rho_0}{\rho}\right)$$.

The correct answer is Option (4): $$mg\left(1 - \frac{\rho_0}{\rho}\right)$$.

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