Question

A small ball of mass M and density $\rho$ is dropped in a viscous liquid of density $\rho_0$. After some time, the ball falls with a constant velocity. What is the viscous force on the ball ?

• A. $F=Mg(1+\frac{\rho_0}{\rho})$
• B. $F=Mg(1+\frac{\rho}{\rho_0})$
• C. $F=Mg(1-\frac{\rho_0}{\rho})$
• D. $F=Mg(1±\rho\rho_0)$

Answer 1

Answer: (C)

$F=Mg(1-\frac{\rho_0}{\rho})$

Answer 2

For constant velocity $F_{net} = 0$
$F_{vis} + \rho_0vg = \rho vg$
$F_{vis} = (\rho - \rho_0)vg$
$=\rho vg(1-\frac{\rho_0}{\rho})$
$=Mg(1-\frac{\rho_0}{\rho})$