$125$ small water drops of same size fall through air with constant terminal velocity $4 \,cm/s$. They coalesce to form a big drop. The terminal velocity of the big drop is: (in $\,m/s$)

When a body falls in air,the resistance of air depends to a great extent on the shape of the body. $3$ different shapes are given in the figure: $(1)$ Disc,$(2)$ Ball,and $(3)$ Cigar-shaped. Identify the combination of air resistances $(R_1, R_2, R_3)$ which truly represents the physical situation. (The cross-sectional areas are the same).

Two spheres of different material are falling through a liquid of density $\rho_L = 2 \times 10^3 \ kg/m^3$ with the same uniform terminal speed. The density of sphere $1$ is $\rho_1 = 8 \times 10^3 \ kg/m^3$ and the density of sphere $2$ is $\rho_2 = 11 \times 10^3 \ kg/m^3$. The ratio of their radii $(r_1/r_2)$ is:

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 . . . . . . $cm/s$.

$A$ 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:

$A$ 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?