A small ball of mass m and density d1 is dropped into a tall vessel of glycerine (density d2) and eventually moves at constant (terminal) velocity. At this stage, what is the magnitude of the viscous (drag) force on the ball?

m*g*(1 - d1/d2)
m*g*(1 - d2/d1)
m*g*(d1/d2 - 1)
m*g*(d2/d1 - 1)

Correct answer: m*g*(1 - d2/d1)

Solution

At terminal velocity: weight = buoyancy + viscous force. So F_viscous = m*g - buoyancy. Buoyancy = V*d2*g where V = m/d1, so buoyancy = (m/d1)*d2*g = m*g*(d2/d1). Therefore F_viscous = m*g - m*g*(d2/d1) = m*g*(1 - d2/d1).

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