$A$ sphere is dropped under gravity through a fluid of viscosity $\eta$. If the average acceleration is half of the initial acceleration,the time to attain the terminal velocity is ($\rho$ = density of sphere; $r$ = radius).

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

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

$A$ 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

$A$ viscous fluid is flowing through a cylindrical tube. The velocity distribution of the fluid is best represented by the diagram

$A$ solid sphere falls with a terminal velocity of $10 \, cm/s$ in the Earth's gravitational field. If it is allowed to fall freely in a region outside the gravitational field of the Earth,the terminal velocity will be: