$A$ 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 $\pi = 22/7$)

If the average terminal velocity of a rain drop is $2 \,m/s$, then the energy transferred by rain to each square metre of the surface at a place which receives $100 \,cm$ of rain in a year is

Two rain drops of same radius '$r$' falling with same terminal velocity '$V$' merge and form a bigger drop of radius '$R$'. The terminal velocity of the big drop is

If a ball of steel (density $\rho = 7.8 \; g \cdot cm^{-3}$) attains a terminal velocity of $10 \; cm \cdot s^{-1}$ when falling in a tank of water (coefficient of viscosity $\eta_{\text{water}} = 8.5 \times 10^{-4} \; Pa \cdot s$),then its terminal velocity in glycerine (density $\rho_{\text{gly}} = 1.2 \; g \cdot cm^{-3}$,coefficient of viscosity $\eta_{\text{gly}} = 13.2 \; Pa \cdot s$) would be nearly:

Why do dust particles settle down on the floor in a closed room? Explain.

$A$ small steel sphere of mass $m$ is falling vertically through a viscous liquid with a constant speed $v$. Which row in the table correctly describes the changes with time in the kinetic energy and gravitational potential energy of the sphere?