The terminal velocity of a small sphere of radius $a$ in a viscous liquid is proportional to

$A$ small sphere of mass $m$ is dropped from a great height. After it has fallen $100 \; m$,it has attained its terminal velocity and continues to fall at that speed. The work done by air friction against the sphere during the first $100 \; m$ of fall is

$n$ small drops of the same size fall through air with a constant terminal velocity of $5 \ cm/s$. If they coalesce to form a single big drop,what is the terminal velocity of the big drop?

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.

$A$ large drop of oil (density $0.8 \, g/cm^3$ and viscosity $\eta_0$) floats up through a column of another liquid (density $1.2 \, g/cm^3$ and viscosity $\eta_L$). Assuming that the two liquids do not mix,the velocity with which the oil drop rises will depend on.

$A$ spherical metal ball of radius $r$ falls through a viscous liquid with terminal velocity $V$. Another metal ball of the same material but of radius $\frac{r}{3}$ falls through the same liquid. What will be its terminal velocity?