Fill in the blanks:
$(i)$ The surface tension of water at critical temperature is ......
$(ii)$ Bernoulli's equation is based on the conservation of ......
$(iii)$ The energy would be ...... if $1$ large drop of water splits into $8$ small drops of water.
$(iv)$ When strong wind passes over a building,the force acting on the building is in the ......

$A$ spray gun is shown in the figure where a piston pushes air out of a nozzle. $A$ thin tube of uniform cross section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle,the liquid from the container rises into the nozzle and is sprayed out. For the spray gun shown,the radii of the piston and the nozzle are $20 \ mm$ and $1 \ mm$ respectively. The upper end of the container is open to the atmosphere.
$1.$ If the piston is pushed at a speed of $5 \ mm \ s^{-1}$,the air comes out of the nozzle with a speed of
$(A)$ $0.1 \ m \ s^{-1}$ $(B)$ $1 \ m \ s^{-1}$ $(C)$ $2 \ m \ s^{-1}$ $(D)$ $8 \ m \ s^{-1}$
$2.$ If the density of air is $\rho_{a}$ and that of the liquid is $\rho_{\ell}$,then for a given piston speed,the rate (volume per unit time) at which the liquid is sprayed will be proportional to
$(A)$ $\sqrt{\frac{\rho_{a}}{\rho_{\ell}}}$ $(B)$ $\sqrt{\rho_{a} \rho_{\ell}}$ $(C)$ $\sqrt{\frac{\rho_{\ell}}{\rho_{a}}}$ $(D)$ $\rho_{\ell}$

$STATEMENT-1$: The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up,but tends to narrow down when held vertically down.
$STATEMENT-2$: In any steady flow of an incompressible fluid,the volume flow rate of the fluid remains constant.

Fill in the blanks:
$(i)$ The cohesive force between the molecules of liquid is more than the adhesive force between the molecules of the plate, then the angle of contact obtained is ...... (acute/obtuse) and the free surface has a shape of ...... (concave/convex).
$(ii)$ The cohesive force between the molecules of liquid is less than the adhesive force between the molecules of the plate, then the angle of contact obtained is ...... (acute/obtuse) and the free surface has a shape of ...... (concave/convex).
$(iii)$ $A$ large pressure is exerted on the surface of a liquid having a shape of .......... (concave/convex).

The human heart discharges $75 \ cc$ of blood per beat against a pressure of $10 \ cm$ of $Hg$. If the heart beats $72$ times per minute,calculate the power of the heart in $W$. (Given: density of $Hg = 13.6 \ g/cc$ and $g = 9.8 \ m/s^2$)

$A$ liquid is kept in a closed vessel. If a glass plate (negligible mass) with a small hole is kept on top of the liquid surface,then the vapour pressure of the liquid in the vessel is