$A$ steel ball is dropped in a viscous liquid. The distance of the steel ball from the top of the liquid is shown in the graph below. The terminal velocity of the ball is closest to .......... $m/s$.

$A$ spherical body of mass $m$ and radius $r$ is allowed to fall in a medium of viscosity $\eta$. The time in which the velocity of the body increases from zero to $0.63$ times the terminal velocity $(v)$ is called the time constant $(\tau)$. Dimensionally,$\tau$ can be represented by:

$A$ spherical ball of radius $1 \ mm$ and density $10.5 \ g/cc$ is dropped in glycerine of coefficient of viscosity $9.8 \ \text{poise}$ and density $1.5 \ g/cc$. The viscous force on the ball when it attains constant velocity is $3696 \times 10^{-x} \ N$. The value of $x$ is $\text{(Given, } g = 9.8 \ m/s^2 \text{ and } \pi = \frac{22}{7}\text{)}$.

The velocity of a small ball of mass $0.3 \, g$ and density $8 \, g/cc$ when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is $1.3 \, g/cc$,then the value of the viscous force acting on the ball will be $x \times 10^{-4} \, N$. The value of $x$ is [use $g = 10 \, m/s^2$]. (in $.125$)

The terminal velocity of a small-sized spherical body of radius $r$ falling vertically in a viscous liquid is given by the proportionality:

Two spherical rain drops reach the surface of the earth with terminal velocities having ratio $16: 9$. The ratio of their surface area is