$A$ small metal sphere of radius $a$ is falling with a velocity $v$ through a vertical column of a viscous liquid. If the coefficient of viscosity of the liquid is $\eta$,then the sphere encounters an opposing force of

If a ball of steel (density $\rho = 7.8 \; g \cdot cm^{-3}$) attains a terminal velocity of $10 \; cm \cdot s^{-1}$ when falling in a tank of water (coefficient of viscosity $\eta_{\text{water}} = 8.5 \times 10^{-4} \; Pa \cdot s$),then its terminal velocity in glycerine (density $\rho_{\text{gly}} = 1.2 \; g \cdot cm^{-3}$,coefficient of viscosity $\eta_{\text{gly}} = 13.2 \; Pa \cdot s$) would be nearly:

$A$ sphere of mass $M$ and radius $R$ is falling in a viscous fluid. The terminal velocity attained by the falling object will be proportional to

The diameter of an air bubble,which was initially $2\,mm$,rises steadily through a solution of density $1750\,kg\,m^{-3}$ at the rate of $0.35\,cm\,s^{-1}$. The coefficient of viscosity of the solution is (in poise,nearest integer). (The density of air is negligible).

$A$ spherical ball of radius $1 \ mm$ and density $10.5 \ g/cc$ is dropped in glycerine of coefficient of viscosity $9.8 \ \text{poise}$ and density $1.5 \ g/cc$. The viscous force on the ball when it attains constant velocity is $3696 \times 10^{-x} \ N$. The value of $x$ is $\text{(Given, } g = 9.8 \ m/s^2 \text{ and } \pi = \frac{22}{7}\text{)}$.

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