A tank is filled with water upto height H . When a hole is made at...

A tank is filled with water upto height

H

. When a hole is made at a distance

h

below the level of water. What will be the horizontal range of water jet? A tank is filled with water upto height H . When a hole is made at a distance h below the level of water. What will be

A tank is filled with water upto height H . When a hole is made at a distance h below the level of water. What will be

Options

A $2 \sqrt{h(H-h)}$
B $4 \sqrt{h(H+h)}$
C $4 \sqrt{h(H-h)}$
D $2 \sqrt{h(H+h)}$

Correct answer

A. $2 \sqrt{h(H-h)}$

Step-by-step solution

Applying Bernoullis' theorem, A tank is filled with water upto height H . When a hole is made at a distance h below the level of water. What will be

the velocity of water at point

v=\sqrt{2 g h}

Time take on to reach point

C

t

So,

\quad H-h=\frac{1}{2} g t^2 t=\sqrt{\frac{2(H-h)}{g}}

...(1) Now horizontal range

\begin{aligned} R & =v t \\ & =\sqrt{2 g h} \times \sqrt{\frac{2(H-h)}{g}}=2 \sqrt{(H-h) h}\end{aligned}

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