What is the velocity $v$ of a metallic ball of radius $r$ falling in a tank of liquid at the instant when its acceleration is one-half that of a freely falling body? (The densities of metal and of liquid are $\rho$ and $\sigma$ respectively,and the viscosity of the liquid is $\eta$).

In the experiment for measurement of viscosity $\eta$ of a given liquid with a ball having radius $R$,consider the following statements.
$A.$ Graph between terminal velocity $V$ and $R$ will be a parabola.
$B.$ The terminal velocities of different diameter balls are constant for a given liquid.
$C.$ Measurement of terminal velocity is dependent on the temperature.
$D.$ This experiment can be utilized to assess the density of a given liquid.
$E.$ If balls are dropped with some initial speed,the value of $\eta$ will change.
Choose the correct answer from the options given below:

Two solid spheres of radii $2 \ mm$ and $4 \ mm$ are tied to the two ends of a light string and released in a liquid of specific gravity $1.3$ and coefficient of viscosity $1 \ Pa \cdot s$. The string is just taut when the two spheres are completely submerged in the liquid. If the density of the materials of the two spheres is $2800 \ kg \cdot m^{-3}$,then the terminal velocity of the system of the spheres is (take $g = 10 \ m \cdot s^{-2}$):

Spherical balls of radius $r$ are falling in a viscous fluid of viscosity $\eta$ with a velocity $v$. The retarding viscous force acting on the spherical ball is

$A$ steel ball of radius $6 \ mm$ has a terminal speed of $12 \ cm s^{-1}$ in a viscous liquid. What will be the terminal speed of a steel ball of radius $3 \ mm$ in the same liquid (in $cm s^{-1}$)?

What is the terminal velocity of a rain drop of radius $0.02 \ mm$ (in $cm \ s^{-1}$)? [Note that the coefficient of viscosity of air is $1.8 \times 10^{-5} \ N \ s \ m^{-2}$, density of water is $1000 \ kg \ m^{-3}$. Use $g = 10 \ m \ s^{-2}$ and density of air can be neglected in comparison with the density of water.]