$A$ 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

Two metal spheres are falling through a liquid of density $2.5 \times 10^3 \ kg/m^3$ with the same uniform speed. The density of the material of the first sphere and the second sphere is $11.5 \times 10^3 \ kg/m^3$ and $8.5 \times 10^3 \ kg/m^3$ respectively. The ratio of the radius of the first sphere to that of the second sphere is

$A$ spherical body of mass $m$ and radius $r$ is allowed to fall in a medium of viscosity $\eta$. The time in which the velocity of the body increases from zero to $0.63$ times the terminal velocity $(v)$ is called the time constant $(\tau)$. Dimensionally,$\tau$ can be represented by:

The terminal velocity of a metallic ball of radius $6 \ mm$ in a viscous fluid is $20 \ cm/s$. The terminal velocity of another ball of same material and having radius $3 \ mm$ in the same fluid will be . . . . . . $cm/s$.

Two uniform solid balls of same density and of radii $r$ and $2r$ are dropped in air and fall vertically downwards. The terminal velocity of the ball with radius $r$ is $1 \, cm \, s^{-1}$. Find the terminal velocity of the ball of radius $2r$ (neglect buoyant force on the balls). ........... $cm \, s^{-1}$

Two rain drops of same radius $r$ falling with terminal velocity $V$ merge and form a bigger drop with radius $R$. The terminal velocity of the bigger drop is: