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

The Correct Option is C

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