$A$ small metal sphere of mass $M$ and density $d_{1}$,when dropped in a jar filled with liquid,moves with terminal velocity after some time. The viscous force acting on the sphere is ($d_{2} =$ density of liquid,$g =$ gravitational acceleration).

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 ......... $cm/s$.

$A$ metal ball of radius $9 \times 10^{-4} \ m$ and density $10^4 \ kg/m^3$ falls freely under gravity through a distance $h$ and enters a tank of water. Considering that the metal ball has constant velocity in water,the value of $h$ is [coefficient of viscosity of water $= 8.1 \times 10^{-4} \ Pa \cdot s, g = 10 \ m/s^2$,density of water $= 10^3 \ kg/m^3$]. (in $m$)

$A$ small spherical ball of radius $0.1 \,mm$ and density $10^{4} \,kg \,m^{-3}$ falls freely under gravity through a distance $h$ before entering a tank of water. If after entering the water the velocity of the ball does not change and it continues to fall with the same constant velocity inside the water,then the value of $h$ will be $m$. (Given $g = 10 \,m \,s^{-2}$,viscosity of water $\eta = 1.0 \times 10^{-5} \,N \,s \,m^{-2}$,density of water $\rho_w = 10^3 \,kg \,m^{-3}$)

Give two uses of Stoke's law.

The terminal velocity $(v_{t})$ of a spherical raindrop depends on the radius $(r)$ of the raindrop as: