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

$A$ ball rises to the surface at a constant velocity in a liquid whose density is $4$ times greater than that of the material of the ball. The ratio of the force of friction acting on the rising ball to its weight is

$A$ spherical solid ball of volume $V$ is made of a material of density $\rho_1$. It is falling through a liquid of density $\rho_2$ $(\rho_2 < \rho_1)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$,i.e.,$F_{viscous} = -kv^2$ $(k > 0)$. The terminal speed of the ball is:

$A$ stone is projected vertically up from the bottom of a water tank. Assuming no water resistance,it will go up and come down in the same time. However,if water drag (resistance) is present,then the time it takes to go up,$t_{up}$,and the time it takes to come down,$t_{down}$,are related as:

Suppose the average mass of raindrops is $3.0 \times 10^{-5} \ kg$ and their average terminal velocity is $9 \ m/s$. Calculate the energy transferred by rain to each square metre of the surface at a place which receives $100 \ cm$ of rain in a year.

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