$A$ large tank is filled with water (density $= 10^3 \ kg/m^3$). $A$ small hole is made at a depth $10 \ m$ below the water surface. The range of water issuing out of the hole is $R$ on the ground. What extra pressure must be applied on the water surface so that the range becomes $2R$? (Take $1 \ atm = 10^5 \ Pa$ and $g = 10 \ m/s^2$)

$A$ 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

$A$ cylinder containing water stands on a table of height $H$. $A$ small hole is punched in the side of the cylinder at its base. The stream of water strikes the ground at a horizontal distance $R$ from the table. Then the depth of water in the cylinder is ............

$A$ 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

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

$A$ cylindrical vessel of height $50 \,cm$ is filled with water and rests on a table. $A$ small hole is made at a height $h$ from the bottom of the vessel so that the water jet hits the table surface at a maximum distance $x_{\max }$ from the vessel as shown in the figure. The value of $x_{\max }$ will be (Neglect the viscosity of water.) (in $\,cm$)