$A$ large open tank has two holes in its wall. One is a square hole of side $a$ at a depth $x$ from the top and the other is a circular hole of radius $r$ at a depth $4x$ from the top. When the tank is completely filled with water,the quantities of water flowing out per second from both holes are the same. Then $r$ is equal to ..........

$A$ tank is filled with water and two holes $A$ and $B$ are made in it. For getting the same range,the ratio of $h^{\prime}$ to $h$ is ..........

$A$ liquid is filled in a tank up to a height of $5 \,m$ and the bottom of the tank is at $5 \,m$ height from the ground. $A$ hole is punched in the tank so that the liquid coming out touches the ground at maximum horizontal distance. Then, the maximum horizontal distance is (in $\,m$)

$A$ cylinder of height $20\;m$ is completely filled with water. The velocity of efflux of water (in $m/s$) through a small hole on the side wall of the cylinder near its bottom is ....... $m/s$.

The water is filled up to a height of $12\, \text{m}$ in a tank having vertical sidewalls. $A$ hole is made in one of the walls at a depth $h$ below the water level. The value of $h$ for which the emerging stream of water strikes the ground at the maximum range is $.....\, \text{m}$.

$A$ container of large uniform cross-sectional area $A$ is resting on a horizontal surface and holds two immiscible,non-viscous,and incompressible liquids of densities $d$ and $2d$,each of height $\frac{H}{2}$,as shown. The upper surface of the liquid with lower density is open to the atmosphere. $A$ small hole is made on the wall of the container at height $h$ $(h < \frac{H}{2})$. The initial speed of efflux of the liquid at the hole is: