$A$ tank is filled up to a height $2H$ with a liquid and is placed on a platform of height $H$ from the ground. The distance $x$ from the ground where a small hole is punched to get the maximum range $R$ is:

$A$ tank with a small hole at the bottom has been filled with water and kerosene (specific gravity $0.8$). The height of water is $3\,m$ and that of kerosene $2\,m$. When the hole is opened,the velocity of fluid coming out from it is nearly ........ $ms^{-1}$. (Take $g = 10\,ms^{-2}$ and density of water $= 10^3\,kg\,m^{-3}$)

$A$ container is filled with water up to a height $h$. $A$ small hole is made at the bottom. What is the ratio of the time taken for the water level to fall from $h$ to $\frac{h}{2}$ to the time taken for it to fall from $\frac{h}{2}$ to $0$?

Water flows into a large tank with a flat bottom at the rate of $10^{-4} \, m^3 s^{-1}$. Water is also leaking out of a hole of area $1 \, cm^2$ at its bottom. If the height of the water in the tank remains steady, then this height is ........ $cm$.

$A$ cubical box of wine has a small spout located in one of the bottom corners. When the box is full and placed on a level surface,opening the spout results in a flow of wine with an initial speed of $v_0$ (see figure). When the box is half empty,someone tilts it at $45^{\circ}$ so that the spout is at the lowest point (see figure). When the spout is opened,the wine will flow out with a speed of

$A$ cylindrical vessel of cross-section $A$ contains water to a height $h$. There is a hole in the bottom of radius $a$. The time in which it will be emptied is