When a body falls in air,the resistance of air depends to a great extent on the shape of the body. $3$ different shapes are given in the figure: $(1)$ Disc,$(2)$ Ball,and $(3)$ Cigar-shaped. Identify the combination of air resistances $(R_1, R_2, R_3)$ which truly represents the physical situation. (The cross-sectional areas are the same).

$A$ raindrop with radius $R=0.2 \, mm$ falls from a cloud at a height $h=2000 \, m$ above the ground. Assume that the drop is spherical throughout its fall and the force of buoyancy may be neglected. The terminal speed attained by the raindrop is: (in $m/s$)
[Density of water $\rho_{w}=1000 \, kg/m^3$,density of air $\rho_{a}=1.2 \, kg/m^3$,$g=10 \, m/s^2$,coefficient of viscosity of air $\eta=1.8 \times 10^{-5} \, Ns/m^2$]

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

In the measurement of viscosity of liquids using terminal velocity experiment, spherical balls of same radius but having different densities are used. The variation of the terminal velocity $(v)$ with the ratio of density of spherical ball $(\sigma)$ to density of the liquid $(\rho)$, is best represented by :

$A$ ball rises to the surface at a constant velocity in a liquid whose density is $4$ times greater than that of the material of the ball. The ratio of the force of friction acting on the rising ball to its weight is

$A$ small ball of mass $M$ and density $\rho$ is dropped in a viscous liquid of density $\rho_0$. After some time,the ball falls with a constant velocity. What is the viscous force on the ball?