$A$ heavy spherical ball is dropped near the surface in a long column of viscous liquid. Which of the following graphs represent the variation of:
$(i)$ Gravitational force with time
$(ii)$ Viscous force with time
$(iii)$ Net force acting on the ball with time

$A$ spherical solid ball of volume $V$ is made up of a material of density $\rho$. It is falling through a liquid of density $\sigma$ $(\sigma < \rho)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of the terminal speed $v_{T}$,$F = -K v_{T}^2$ $(K > 0)$. Then,the terminal speed of the ball is ($g =$ acceleration due to gravity).

$A$ rain drop of diameter $1 \ mm$ falls with a terminal velocity of $0.7 \ ms^{-1}$ in air. If the coefficient of viscosity of air is $2 \times 10^{-5} \ Pa \cdot s$, the viscous force on the rain drop is

Eight identical drops of same radii are falling through air with steady velocity $6 \ cm/s$. If these drops coalesce,then the terminal velocity would be .......... $cm/s$.

$A$ ball of density $\rho$ is released from deep inside a viscous liquid of density $2\rho$. It will move up:

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
$(A)$ $\frac{|\overrightarrow{V}_{P}|}{|\overrightarrow{V}_{Q}|}=\frac{\eta_1}{\eta_2}$
$(B)$ $\frac{|\overrightarrow{V}_{P}|}{|\overrightarrow{V}_{Q}|}=\frac{\eta_2}{\eta_1}$
$(C)$ $\overrightarrow{V}_{P} \cdot \overrightarrow{V}_{Q} > 0$
$(D)$ $\overrightarrow{V}_{P} \cdot \overrightarrow{V}_{Q} < 0$