$A$ ball rises to the surface of a liquid with constant velocity. The density of the liquid is four times the density of the material of the ball. The viscous force of the liquid on the rising ball is greater than the weight of the ball by a factor of

Two drops of equal radius are falling through air with a steady velocity of $5\,cm/s$. If the two drops coalesce,then its terminal velocity will be

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

$A$ spherical liquid drop of radius $r$ acquires the terminal velocity $v_1$ when falling through a gas of viscosity $\eta$. Now the drop is broken into $64$ identical droplets and each droplet acquires terminal velocity $v_2$ falling through the same gas. The ratio of terminal velocities $v_1/v_2$ is . . . . . . .

An iron sphere of mass $20 \times 10^{-3} \ kg$ falls through a viscous liquid with terminal velocity $0.5 \ ms^{-1}$. The terminal velocity (in $ms^{-1}$) of another iron sphere of mass $54 \times 10^{-2} \ kg$ is (in $.5$)

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