Give two uses of Stoke's law.

Eight equal drops of water,each of radius $r = 2 \ mm$,are falling through air with a terminal velocity of $16 \ cm/s$. The eight drops combine to form a single big drop. The terminal velocity of the bigger drop will be $.... \ cm/s$.

The velocity of a small ball of mass $M$ and density $d_1$ when dropped in a container filled with glycerin becomes constant after some time. If the density of glycerin is $d_2$,the viscous force acting on the ball is ($g$ = acceleration due to gravity).

$A$ spherical solid ball of volume $V$ is made of a material of density $\rho_1$. It is falling through a liquid of density $\rho_2$ $(\rho_2 < \rho_1)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$,i.e.,$F_{viscous} = -kv^2$ $(k > 0)$. The terminal speed of the ball is:

State Stokes' law. By using it,deduce the expression for:
$(i)$ Initial acceleration of a smooth sphere.
$(ii)$ Equation of terminal velocity of a sphere falling freely through a viscous medium.
$(iii)$ Explain: Upward motion of bubbles produced in a fluid.

If the terminal velocity of a metal sphere of mass $8 \ g$ falling through a liquid is $3 \ cm s^{-1}$,then the terminal velocity of another sphere of mass $64 \ g$ made of the same metal falling through the same liquid is (in $cm s^{-1}$)