$A$ lead shot of $1 \, mm$ diameter falls through a long column of glycerine. The variation of its velocity $v$ with distance covered is represented by:

The terminal velocity $v$ of a spherical ball of lead of radius $R$ falling through a viscous liquid varies with $R$ such that

Why do rain drops not possess a velocity greater than a certain limit? Explain.

$A$ 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 $\rho_w = 10^3 \,kg \,m^{-3}$)

Small water droplets of radius $0.01 \,mm$ are formed in the upper atmosphere and falling with a terminal velocity of $10 \,cm/s$. Due to condensation, if $8$ such droplets are coalesced to form a larger drop, the new terminal velocity will be ........... $cm/s$.

Give the practical uses of viscosity.