A small ball of mass M and density ρ is dropped in a viscous liquid of density ρ 0 . After some time, the ball falls with a constant velocity. What is the viscous force on the ball?

Step-by-step solution

The buoyant force is given by B = V ρ 0 g where V is the volume of the ball. The weight of the ball W = M g = V ρ g , is acting in the opposite direction of the buoyant force . Hence, at terminal velocity M g - B = F v ⇒ B + F v = M g ⇒ F v = V ρ g - V ρ 0 g ⇒ F v = ρ V g ( 1 - ρ 0 ρ ) ⇒ F v = M g ( 1 - ρ 0 ρ )