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PART - 2 CH - 9 Mechanical Properties of Fluids — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsPART - 2 CH - 9 Mechanical Properties of Fluids3 Marks
Question
A tank is filled with water up to a height of H meter and there is a hole in it at a height from the bottom. Find the volume of water coming out of that hole and how far from the tank will it fall on the ground?
✓

Answer

The water tank is filled to a height of H meter.
The hole from the bottom is at a height of $h$ $m $.
Height from water surface to surface
$=( H - h)$ $m$
Velocity of water coming out of that hole
$\begin{aligned}v & =\sqrt{2 g \times(H-h)} \\v & =\sqrt{2 g(H-h)}\end{aligned}$
Let the distance from tank is $x ~ m$ and the time of fall is $t ~\text sec$.
$\begin{aligned}h & =u t+\frac{1}{2} g t^2 \\h & =0+\frac{1}{2} g t^2 \\t^2 & =2 h / g \\t & =\sqrt{\frac{2 h}{g}}\end{aligned}$
The horizontal distance covered by the velocity $v$ in the same time will be
$\begin{aligned}x & =v t \\& =\sqrt{2 g(H-h)} \times \sqrt{\frac{2 h}{g}} \\x & =2 \sqrt{h(H-h)}\end{aligned}$
Hence, it will fall at a distance of $2 \sqrt{( H - h)}$ from the tank.

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