The velocity of a small ball of mass $M$ and density $d_1$ when dropped in a container filled with glycerin becomes constant after some time. If the density of glycerin is $d_2$,the viscous force acting on the ball is ($g$ = acceleration due to gravity).

Eight spherical rain drops of the same mass and radius are falling down with a terminal speed of $6 \,cm \,s^{-1}$. If they coalesce to form one big drop,what will be the terminal speed of the bigger drop? (Neglect the buoyancy of the air)

Spherical balls of radius $r$ are falling in a viscous fluid of viscosity $\eta$ with a velocity $v$. The retarding viscous force acting on the spherical ball is

In an experiment,a small steel ball falls through a liquid at a constant speed of $10\, cm/s$. If the steel ball is pulled upward with a force equal to twice its effective weight,how fast will it move upward? ......... $cm/s$

Two rain drops reach the earth with different terminal velocities having ratio $9:4$. Then the ratio of their volumes is

$A$ solid sphere of radius $R$ acquires a terminal velocity $\nu_1$ when falling (due to gravity) through a viscous fluid having a coefficient of viscosity $\eta$. The sphere is broken into $27$ identical solid spheres. If each of these spheres acquires a terminal velocity $\nu_2$ when falling through the same fluid,the ratio $(\nu_1/\nu_2)$ equals: