Properties of Matter

A spherical solid ball of volume $V$ is made of a material of density ${\rho _1}$. It is falling through a liquid of density ${\rho _2}\left( {{\rho _2} < {\rho _1}} \right)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v,$ i.e., ${F_{viscous}} = - k{v^2}\left( {k > 0} \right).$ The terminal speed of the ball is