(C) The velocity of efflux of the liquid from the hole is given by Torricelli's law: $v = \sqrt{2gd}$.The vertical height through which the water fall

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(C) The velocity of efflux of the liquid from the hole is given by Torricelli's law: $v = \sqrt{2gd}$.The vertical height through which the water falls is $h$.The time taken for the water to reach the ground is calculated using the equation of motion $h = \frac{1}{2}gt^2$,which gives $t = \sqrt{\frac{2h}{g}}$.The horizontal range $R$ is the product of the horizontal velocity and the time of flight:$R = v \times t = \sqrt{2gd} \times \sqrt{\frac{2h}{g}}$.Squaring both sides,we get $R^2 = 2gd \times \frac{2h}{g} = 4dh$.Therefore,the depth $d$ is given by $d = \frac{R^2}{4h}$.

Class 11 Physics Fluid Mechanics and Surface Tension Velocity of Efflux and Torricelli's law

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$A$ water barrel having water up to a depth $d$ is placed on a table of height $h$. $A$ small hole is made on the wall of the barrel at its bottom. If the stream of water coming out of the hole falls on the ground at a horizontal distance $R$ from the barrel,then the value of $d$ is

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A
$\frac{4 h}{R^2}$
B
$4 h R^2$
C
$\frac{R^2}{4 h}$
D
$\frac{h}{4 R^2}$

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Fluid Mechanics and Surface Tension

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Velocity of Efflux and Torricelli's law

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MediumJEE MAIN 2019

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$A$ water barrel having water up to a depth $d$ is placed on a table of height $h$. $A$ small hole is made on the wall of the barrel at its bottom. If the stream of water coming out of the hole falls on the ground at a horizontal distance $R$ from the barrel,then the value of $d$ is

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$A$ 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:

If in a stationary lift,a man is standing with a bucket full of water,having a hole at its bottom. The rate of flow of water through this hole is $R_0$. If the lift starts to move up and down with the same acceleration $a$,and the rates of flow of water are $R_u$ and $R_d$ respectively,then:

$A$ cylindrical vessel of $90 \ cm$ height is kept filled up to the brim. It has four holes $1, 2, 3, 4$ which are respectively at heights of $20 \ cm, 30 \ cm, 45 \ cm,$ and $50 \ cm$ from the horizontal floor $PQ.$ The water falling at the maximum horizontal distance from the vessel comes from:

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