The terminal velocity $v$ of a spherical ball of lead of radius $R$ falling through a viscous liquid varies with $R$ such that

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

$125$ 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 $\,m/s$)

The average mass of rain drops 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.

$A$ sphere is dropped under gravity through a fluid of viscosity $\eta$. If the average acceleration is half of the initial acceleration,the time to attain the terminal velocity is ($\rho$ = density of sphere; $r$ = radius).

$A$ small spherical solid ball is dropped from a great height in a viscous liquid. Its journey in the liquid is best described in the diagram given below by the