$A$ vessel containing water is moving with a constant speed towards the right along a straight horizontal path. Which of the following diagrams represents the surface of the liquid?

$A$ 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
$(A)$ $\sqrt{\frac{\rho_{a}}{\rho_{\ell}}}$ $(B)$ $\sqrt{\rho_{a} \rho_{\ell}}$ $(C)$ $\sqrt{\frac{\rho_{\ell}}{\rho_{a}}}$ $(D)$ $\rho_{\ell}$

An open cubical tank was initially fully filled with water. When the tank was accelerated on a horizontal plane along one of its sides,it was found that one-third of the volume of water spilled out. The acceleration was:

$A$ river of salty water is flowing with a velocity $2 \,m/s$. If the density of the water is $1.2 \,g/cc$, then the kinetic energy of each cubic metre of water is

An incompressible liquid is kept in a container having a weightless piston with a hole. $A$ capillary tube of inner radius $0.1 \,mm$ is dipped vertically into the liquid through the airtight piston hole,as shown in the figure. The air in the container is isothermally compressed from its original volume $V_0$ to $\frac{100}{101} V_0$ with the movable piston. Considering air as an ideal gas,the height $(h)$ of the liquid column in the capillary above the liquid level in $cm$ is. . . . . . .
[Given: Surface tension of the liquid is $0.075 \,N \,m^{-1}$,atmospheric pressure is $10^5 \,N \,m^{-2}$,acceleration due to gravity $(g)$ is $10 \,m \,s^{-2}$,density of the liquid is $10^3 \,kg \,m^{-3}$ and contact angle of capillary surface with the liquid is zero]

An air bubble of volume $50\, cm^3$ is formed at the bottom of a lake $47.6\, m$ deep. What will be its volume when it reaches the surface? (Atmospheric pressure $= 70\, cm$ of $Hg$ and density of $Hg = 13.6\, g/cm^3$)