$A$ liquid drop of density $Q$ is floating half-immersed in a liquid of density $d$. What is the diameter of the liquid drop? ($Q$ > $d$, $g = $ acceleration due to gravity, $T = $ surface tension)

Match the columns $I$ and $II$:

Column $I$	Column $II$
$A$. Stoke's law	$I$. Pressure and energy
$B$. Turbulence	$II$. Hydraulic lift
$C$. Bernoulli's Principle	$III$. Viscous drag
$D$. Pascal's law	$IV$. Reynold's number

The correct match is:

Fill in the blanks using the word$(s)$ from the list appended with each statement:
$(a)$ Surface tension of liquids generally . . . with temperatures (increases / decreases)
$(b)$ Viscosity of gases . . . with temperature,whereas viscosity of liquids . . . with temperature (increases / decreases)
$(c)$ For solids with elastic modulus of rigidity,the shearing force is proportional to . . .,while for fluids it is proportional to . . . (shear strain / rate of shear strain)
$(d)$ For a fluid in a steady flow,the increase in flow speed at a constriction follows (conservation of mass / Bernoulli's principle)
$(e)$ For the model of a plane in a wind tunnel,turbulence occurs at a . . . speed for turbulence for an actual plane (greater / smaller)

State whether the following statements are True or False:
$(i)$ If the weight of a body is greater than the buoyant force of the liquid,the body floats on the surface of the liquid.
$(ii)$ The velocity of water at the bottom of a river is always slower than at the surface.
$(iii)$ The angle of contact increases with an increase in the temperature of the liquid.

$27$ equal small water drops combine to form a big drop. If the surface tension of water is $T$ and the radius of a small drop is $r$,then:
$(A)$ The excess pressure inside the big drop is three times the excess pressure inside the small drop.
$(B)$ Surface energy decreases in this process.
$(C)$ In this process,$72 \pi r^2 T$ energy is released.
$(D)$ The radius of the big drop is $3r$.
The true statements are:

Vapour is injected at a uniform rate into a closed vessel which was initially evacuated. The pressure in the vessel: