Sixty-four spherical rain drops of equal size are falling vertically through air with a terminal velocity of $1.5 \ m/s$. All of the drops coalesce to form a single big spherical drop. The terminal velocity of the big drop is ........... $m/s$.

In the measurement of viscosity of liquids using terminal velocity experiment, spherical balls of same radius but having different densities are used. The variation of the terminal velocity $(v)$ with the ratio of density of spherical ball $(\sigma)$ to density of the liquid $(\rho)$, is best represented by :

The displacement of a ball falling from rest in a viscous medium is plotted against time. Choose a possible option.

$A$ small steel ball is dropped into a long cylinder containing glycerine. Which one of the following is the correct representation of the velocity-time graph for the transit of the ball?

Two solid spheres of radii $2 \ mm$ and $4 \ mm$ are tied to the two ends of a light string and released in a liquid of specific gravity $1.3$ and coefficient of viscosity $1 \ Pa \cdot s$. The string is just taut when the two spheres are completely submerged in the liquid. If the density of the materials of the two spheres is $2800 \ kg \cdot m^{-3}$,then the terminal velocity of the system of the spheres is (take $g = 10 \ m \cdot s^{-2}$):

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: