Sixty-four rain drops of radius $1 \ mm$ each,falling down with a terminal velocity of $10 \ cm/s$,coalesce to form a bigger drop. The terminal velocity of the bigger drop is . . . . . . $cm/s$.

In Millikan's oil drop experiment, a charged drop falls with terminal velocity $V$. If an electric field $E$ is applied in a vertically upward direction, then it starts moving in an upward direction with terminal velocity $2V$. If the magnitude of the electric field is decreased to $E/2$, then the terminal velocity will become

$A$ raindrop with radius $R=0.2 \, mm$ falls from a cloud at a height $h=2000 \, m$ above the ground. Assume that the drop is spherical throughout its fall and the force of buoyancy may be neglected. The terminal speed attained by the raindrop is: (in $m/s$)
[Density of water $\rho_{w}=1000 \, kg/m^3$,density of air $\rho_{a}=1.2 \, kg/m^3$,$g=10 \, m/s^2$,coefficient of viscosity of air $\eta=1.8 \times 10^{-5} \, Ns/m^2$]

$A$ small spherical ball of radius $r$,falling through a viscous medium of negligible density has terminal velocity $v$. Another ball of the same mass but of radius $2r$,falling through the same viscous medium will have terminal velocity:

Two spheres $P$ and $Q$ of equal radii have densities $\rho_1$ and $\rho_2$,respectively. The spheres are connected by a massless string and placed in liquids $L_1$ and $L_2$ of densities $\sigma_1$ and $\sigma_2$ and viscosities $\eta_1$ and $\eta_2$,respectively. They float in equilibrium with the sphere $P$ in $L_1$ and sphere $Q$ in $L_2$ and the string being taut (see figure). If sphere $P$ alone in $L_2$ has terminal velocity $\overrightarrow{V}_{P}$ and $Q$ alone in $L_1$ has terminal velocity $\overrightarrow{V}_{Q}$,then
$(A)$ $\frac{|\overrightarrow{V}_{P}|}{|\overrightarrow{V}_{Q}|}=\frac{\eta_1}{\eta_2}$
$(B)$ $\frac{|\overrightarrow{V}_{P}|}{|\overrightarrow{V}_{Q}|}=\frac{\eta_2}{\eta_1}$
$(C)$ $\overrightarrow{V}_{P} \cdot \overrightarrow{V}_{Q} > 0$
$(D)$ $\overrightarrow{V}_{P} \cdot \overrightarrow{V}_{Q} < 0$

Two spheres of the same material,but of radii $R$ and $3R$ are allowed to fall vertically downwards through a liquid of density $\rho$. The ratio of their terminal velocities is