When an air bubble of radius $r$ rises from the bottom to the surface of a lake,its radius becomes $5r/4$ (the pressure of the atmosphere is equal to the $10 \, m$ height of water column). If the temperature is constant and the surface tension is neglected,the depth of the lake is .... $m$ (in $.53$)

Water flows through a frictionless duct with a cross-section varying as shown in the figure. Pressure $p$ at points along the axis is represented by:

$A$ liquid of density $\rho$ is coming out of a hose pipe of cross-sectional area $A$ with horizontal speed $v$ and hits a mesh. $50\%$ of the liquid passes through the mesh unaffected. $25\%$ loses all of its momentum and $25\%$ comes back with the same speed. The resultant pressure on the mesh will be

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

Which of the following phenomena is not due to surface tension?

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