$A$ light cylindrical vessel is kept on a horizontal surface. The area of the base is $A$. $A$ hole of cross-sectional area $a$ is made just at its bottom side. The minimum coefficient of friction necessary to prevent the vessel from sliding due to the impact force of the emerging liquid is $(a \ll A)$.

Consider a water jar of radius $R$ that has water filled up to height $H$ and is kept on a stand of height $h$ (see figure). Through a hole of radius $r$ $(r << R)$ at its bottom,the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is $x$,then:

$A$ cylindrical tank has a hole of area $2 \,cm^2$ at its bottom. If water is poured into the tank from a tube above it at the rate of $100 \,cm^3 \,s^{-1}$, then the maximum height up to which water can rise in the tank is (Acceleration due to gravity, $g=10 \,ms^{-2}$) (in $cm$)

$A$ cylindrical tank has a hole of $1 \, cm^2$ in its bottom. If water is allowed to flow into the tank from a tube above it at the rate of $70 \, cm^3/sec$, then the maximum height up to which water can rise in the tank is .......... $cm$.

There are two holes,one each along the opposite sides of a wide rectangular tank. The cross-section of each hole is $0.01 \,m^2$ and the vertical distance between the holes is $1 \,m$. The tank is filled with water. The net force on the tank in newton when the water flows out of the holes is (Density of water $= 1000 \,kg/m^3$,$g = 10 \,m/s^2$)

$A$ 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