$A$ small ball of mass $M$,radius $R$ and density $\rho$ moves with terminal velocity through a container filled with glycerine of density $\sigma$. The viscous force acting on the ball is ($g=$ gravitational acceleration).

$A$ solid metallic sphere of radius $r$ is allowed to fall freely through air. If the frictional resistance due to air is proportional to the cross-sectional area and to the square of the velocity,then the terminal velocity of the sphere is proportional to which of the following?

Two drops of equal radius are falling with a terminal velocity of $5 \, cm/s$. If they coalesce to form a single larger drop,what will be the terminal velocity of the new drop?

From amongst the following curves, which one shows the variation of the velocity $v$ with time $t$ for a small-sized spherical body falling vertically in a long column of a viscous liquid?

Two metal spheres are falling through a liquid of density $2.5 \times 10^3 \ kg/m^3$ with the same uniform speed. The density of the material of the first sphere and the second sphere is $11.5 \times 10^3 \ kg/m^3$ and $8.5 \times 10^3 \ kg/m^3$ respectively. The ratio of the radius of the first sphere to that of the second sphere is

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).