A spherical ball is dropped in a long column of a highly viscous liquid. The curve in the graph shown, which represents the speed of the ball $(v)$ as a function of time $(t)$ is 

A spherical solid ball of volume $V$ is made of a material of density $\rho_1$ . It is falling through a liquid of density $\rho_2 (\rho_2 < \rho_1 )$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$, i.e., $F_{viscous}= -kv^2 (k >0 )$,The terminal speed of the ball is 

Two small spherical metal balls, having equal masses, are made from materials of densities $\rho_{1}$ and $\rho_{2}\left(\rho_{1}=8 \rho_{2}\right)$ and have radii of $1\; \mathrm{mm}$ and $2\; \mathrm{mm}$, respectively. They are made to fall vertically (from rest) in a viscous medum whose coefficient of viscosity equals $\eta$ and whose denstry is $0.1 \mathrm{\rho}_{2} .$ The ratio of their terminal velocitites would be 

Write the equation of terminal velocity.

Which of the following option correctly describes the variation of the speed $v$  and acceleration $'a'$  of a point mass falling vertically in a viscous medium that applies a force $F = -kv,$ where $'k'$  is a constant, on the body? (Graphs are schematic and not drawn to scale)

The terminal velocity $\left( v _{ t }\right)$ of the spherical rain drop depends on the radius ( $r$ ) of the spherical rain drop as