Water is filled in a cylindrical vessel of height $H$. $A$ hole is made at height $z$ from the bottom, as shown in the figure. The value of $z$ for which the range $(R)$ of the emerging water through the hole will be maximum is:

$A$ vertical tank,open at the top,is filled with a liquid and rests on a smooth horizontal surface. $A$ small hole is opened at the centre of one side of the tank. The area of cross-section of the tank is $N$ times the area of the hole,where $N$ is a large number. Neglect the mass of the tank itself. The initial acceleration of the tank is:

$A$ large tank filled with water to a height $h$ is to be emptied through a small hole at the bottom. The ratio of times taken for the level of water to fall from $h$ to $h/2$ and from $h/2$ to $0$ is

$A$ tank filled with fresh water has a hole in its bottom and water is flowing out of it. If the size of the hole is increased,then

For the shown diagram,find the ratio of $R_1: R_2$.

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 $.....\, \text{m}$.