$A$ vessel containing a liquid has a constant acceleration of $19.6 \, m/s^2$ in the horizontal direction. The free surface of the water gets sloped with the horizontal at an angle of ..........

Different processes are given in Column-$I$ and their reasons are given in Column-$II$. Match them appropriately.

Column-$I$	Column-$II$
$(a)$ Rain drops move downwards with constant velocity.	$(i)$ Viscous liquids
$(b)$ Floating clouds at a height in air.	$(ii)$ Viscosity
	$(iii)$ Less density

$(a)$ It is known that the density $\rho$ of air decreases with height $y$ as $\rho = \rho_{0} e^{-y / y_{0}}$,where $\rho_{0} = 1.25 \; kg \, m^{-3}$ is the density at sea level,and $y_{0}$ is a constant. This density variation is called the law of atmospheres. Obtain this law assuming that the temperature of the atmosphere remains constant (isothermal conditions). Also,assume that the value of $g$ remains constant.
$(b)$ $A$ large $He$ balloon of volume $1425 \; m^{3}$ is used to lift a payload of $400 \; kg$. Assume that the balloon maintains a constant radius as it rises. How high does it rise?
[Take $y_{0} = 8000 \; m$ and $\rho_{He} = 0.18 \; kg \, m^{-3}$]

Why is skating possible on ice?

Two identical cylindrical vessels with their bases at the same level, each contains a liquid of density $d$. The height of the liquid in one vessel is $h_1$ and that in the other vessel is $h_2$. The area of either base is $A$. The work done by gravity in equalizing the levels when the two vessels are connected is

$A$ capillary tube $(A)$ is dipped in water. Another identical tube $(B)$ is dipped in a soap-water solution. Which of the following shows the relative nature of the liquid columns in the two tubes?