Two vessels of equal cross-sectional area $A$ are filled with a liquid of density $d$. The height of the liquid in one vessel is $h_1$ and in the other vessel is $h_2$. When both vessels are connected,find the work done by gravity.

State whether the following statements are True or False:
$(i)$ The Bernoulli equation can be considered to be a statement of the conservation of energy.
$(ii)$ The angle of contact between a drop of water and the material of a raincoat is an acute angle.
$(iii)$ The absence of roughness between two consecutive layers of fluid is the definition of viscosity.

$A$ ball is made of a material of density $\rho$ where $\rho_{\text{oil}} < \rho < \rho_{\text{water}}$,with $\rho_{\text{oil}}$ and $\rho_{\text{water}}$ representing the densities of oil and water,respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water,which of the following pictures represents its equilibrium position?

Drops of liquid of density $d$ are floating half immersed in a liquid of density $\rho$. If the surface tension of the liquid is $T$, then the radius of the drop is

An air bubble of volume $1\,cm^3$ rises from the bottom of a lake $40\,m$ deep to the surface at a temperature of $12^{\circ}C$. The atmospheric pressure is $1 \times 10^5\,Pa$,the density of water is $1000\,kg/m^3$,and $g = 10\,m/s^2$. There is no difference in the temperature of water at the depth of $40\,m$ and on the surface. The volume of the air bubble when it reaches the surface will be $..........\,cm^3$. (in $,cm^3$)

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