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 (in $cm \ s^{-1}$)? (Neglect the buoyancy of the air)

$A$ 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 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).

The terminal velocity of a sphere of radius $3 \ mm$ falling in a viscous liquid is $10 \ cm/s$. The terminal velocity of a ball of radius $6 \ mm$ of the same material falling in the same liquid will be $...... \ cm/s$.

On which factors does terminal velocity depend? Explain.

Consider two solid spheres $P$ and $Q$ each of density $8 \ g \ cm^{-3}$ and diameters $1 \ cm$ and $0.5 \ cm$,respectively. Sphere $P$ is dropped into a liquid of density $0.8 \ g \ cm^{-3}$ and viscosity $\eta = 3 \ \text{poiseuille}$. Sphere $Q$ is dropped into a liquid of density $1.6 \ g \ cm^{-3}$ and viscosity $\eta = 2 \ \text{poiseuille}$. The ratio of the terminal velocities of $P$ and $Q$ is: