$A$ ball rises to the surface of a liquid with constant velocity. The density of the liquid is four times the density of the material of the ball. The viscous force of the liquid on the rising ball is greater than the weight of the ball by a factor of

$A$ small spherical ball of radius $r$,falling through a viscous medium of negligible density has terminal velocity $v$. Another ball of the same mass but of radius $2r$,falling through the same viscous medium will have terminal velocity:

$A$ 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 $(v_t)$ is called the time constant $(\tau)$. Dimensionally,$\tau$ can be represented by:

Two identical drops of water are falling through air with steady velocity $V$. If the two drops coalesce to form a single drop,what is the new terminal velocity of the single drop?

Eight identical drops of same radii are falling through air with steady velocity $6 \ cm/s$. If these drops coalesce,then the terminal velocity would be .......... $cm/s$.

$A$ particle released from rest is falling through a thick fluid under gravity. The fluid exerts a resistive force on the particle proportional to the square of its speed. Which one of the following graphs best depicts the variation of its speed $v$ with time $t$ ?