An air bubble rises from the bottom of a water tank of height $5 \ m$. If the initial volume of the bubble is $3 \ mm^3$, what will be its volume as it reaches the surface (in $mm^3$)? Assume that its temperature does not change. $[g=9.8 \ m \ s^{-2}, 1 \ atm=10^5 \ Pa, \text{density of water}=1 \ g/cm^3]$

Consider the following statements:
$A.$ Surface tension arises due to extra energy of the molecules at the surface as compared to the molecules in the interior of a liquid.
$B.$ As the temperature of a liquid rises, the coefficient of viscosity increases.
$C.$ As the temperature of a gas increases, the coefficient of viscosity increases.
$D.$ The onset of turbulence is determined by Reynolds number.
$E.$ In a steady flow, two streamlines never intersect.
Choose the correct answer from the options given below:

Water coming out of a horizontal tube at a speed $v$ strikes a vertical wall normally,close to the mouth of the tube,and falls down vertically after impact. When the speed of water is increased to $2v$:

$A$ bucket contains water filled up to a height $h = 15 \ cm$. The bucket is tied to a rope which is passed over a frictionless light pulley,and the other end of the rope is tied to a weight of mass which is half of that of the (bucket $+$ water). The water pressure above atmospheric pressure at the bottom is ....... $kPa$.

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

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