$A$ 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 $\,cm$)

$A$ cylindrical tank with a large diameter is filled with water. Water drains out through a hole at the bottom of the tank. If the cross-sectional area of the hole is $6 \ cm^2$, then the drainage rate in $m^3 s^{-1}$ when the depth of the water is $0.2 \ m$ is:

Water flows out of a hole on the side of a bucket and follows a parabolic path. If the bucket falls freely under gravity, ignoring air resistance, the water flow

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

$A$ rectangular tank is placed on a horizontal ground and is filled with water to a height $H$ above the base. $A$ small hole is made on one vertical side at a depth $D$ below the level of the water in the tank. The distance $x$ from the bottom of the tank at which the water jet from the tank will hit the ground is

$A$ 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