The terminal velocity of a small sphere of radius $a$ in a viscous liquid is proportional to

$A$ solid metal sphere released in a vertical liquid column has attained terminal velocity in the downward direction. The magnitudes of viscous force, buoyant force, and gravitational force acting on it are $F_{v}$, $F_{B}$, and $F_{W}$ respectively. Then, the correct relation between them is:

State Stokes' law. By using it,deduce the expression for:
$(i)$ Initial acceleration of a smooth sphere.
$(ii)$ Equation of terminal velocity of a sphere falling freely through a viscous medium.
$(iii)$ Explain: Upward motion of bubbles produced in a fluid.

$A$ metal sphere of mass $m$ and density $\sigma_1$ falls with terminal velocity through a container containing liquid. The density of the liquid is $\sigma_2$. The viscous force acting on the sphere is:

The velocity of a small ball of mass $M$ and density $d$,when dropped in a container filled with glycerine,becomes constant after some time. If the density of glycerine is $\frac{d}{2}$,then the viscous force acting on the ball will be:

The speed of a ball of radius $2 \,cm$ in a viscous liquid is $20 \,cm / s$. What will be the speed of a ball of radius $1 \,cm$ in the same liquid (in $\,cm / s$)?