Water is filled in a container up to a height of $3\,m$. $A$ small hole of area $A_0$ is punched in the wall of the container at a height of $52.5\,cm$ from the bottom. The cross-sectional area of the container is $A$. If $A_0/A = 0.1$,then $v^2$ is......... $m^2/s^2$ (where $v$ is the velocity of water coming out of the hole).

Equal volumes of two immiscible liquids of densities $\rho$ and $2\rho$ are filled in a vessel as shown in the figure. Two small holes are punched at depths $h/2$ and $3h/2$ from the surface of the lighter liquid. If $v_1$ and $v_2$ are the velocities of efflux at these two holes,then $v_1/v_2$ is:

Consider the configuration of a stationary water tank of cross-sectional area $A_{0}$ and a small bucket as shown in the figure below. What is the speed $v$ (in $m/s$) of the bucket so that the water leaking out of a hole of cross-sectional area $A$ (as shown) from the water tank does not fall outside the bucket? (Take $h=5 \, m$,$H=5 \, m$,$g=10 \, m/s^{2}$,$A=5 \, cm^{2}$,and $A_{0}=500 \, cm^{2}$).

$A$ tank with vertical walls is mounted so that its base is at a height $H$ above the horizontal ground. The tank is filled with water to a depth $h$. $A$ hole is punched in the side wall of the tank at a depth $x$ below the water surface. To have maximum range of the emerging stream,the value of $x$ is

$A$ cylindrical vessel filled with water up to the height $H$ becomes empty in time $t_0$ due to a small hole at the bottom of the vessel. If water is filled to a height $4H$,it will flow out in time:

$A$ vessel completely filled with water has two holes $P$ and $Q$ at depths $2h$ and $8h$ from the top,respectively. Hole $P$ is a square of side $a$ and hole $Q$ is a circle of radius $r$. If the volume of water flowing out per second from both holes is the same,then the side $a$ of hole $P$ is: