The height of water in a tank is $H$. The range of the liquid emerging out from a hole in the wall of the tank at a depth $\frac{3H}{4}$ from the upper surface of water will be:

$A$ cylindrical vessel of cross-sectional area $1000 \ cm^2$ is fitted with a frictionless piston of mass $10 \ kg$ and filled with water completely. $A$ small hole of cross-sectional area $10 \ mm^2$ is opened at a point $50 \ cm$ deep from the lower surface of the piston. The velocity of efflux from the hole will be ........... $m/s$.

$A$ fully filled open water tank has two holes on either side of its walls. One is a square hole of side $x \,cm$ at a depth of $2 \,m$ from the top, and the other hole is an equilateral triangle of side $4 \,cm$ at a depth of $6 \,m$ from the top. If the rate of flow of water is the same from both the holes, then the value of $x$ is: (in $\,cm$)

$A$ cylindrical tank has a hole of $1 \ cm^2$ in its bottom. If the water is allowed to flow into the tank from a tube above it at the rate of $70 \ cm^3/s$,then the maximum height up to which water can rise in the tank is: $(g = 9.8 \ m/s^2)$ (in $cm$)

Water is filled in a tank up to a height of $20 \ cm$ from the bottom of the tank. Water flows through a hole of area $1 \ mm^2$ at its bottom. The mass of the water coming out from the hole in a time of $0.6 \ s$ is (Density of water $= 1000 \ kg \ m^{-3}$ and acceleration due to gravity $= 10 \ m \ s^{-2}$) (in $g$)

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 $= 1000 \,kg/m^3$, $g = 10 \,m/s^2$)