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  • A cylindrical tank of height H is completely filled with water. On its vertical side there are two tiny holes, one above the middle at a height <img alt="\mathrm{h_1}" src="https://entrancecor

A cylindrical tank of height H is completely filled with water. On its vertical side there are two tiny holes, one above the middle at a height \mathrm{h_1} and the other below the middle at a depth \mathrm{h_2}. If the jets of water from the holes meet at the same point at the horizontal plane through the bottom of the tank then the ratio \mathrm{\frac{h_1}{h_2}} is

Option: 1

1


Option: 2

2


Option: 3

3


Option: 4

4


Answers (1)

best_answer

The horizontal range of a jet of water emerging from a hole at a height h below the surface of water is given by

                                                   \mathrm{ R=2 \sqrt{h(H-h)} }

The upper hole is at a height\mathrm{ \left(\frac{H}{2}+h_1\right)} from the bottom and the lower hole is at a height \mathrm{ \left(\frac{H}{2}-h_2\right)} from the bottom. Their depths from the surface are respectively \mathrm{ \left(\frac{H}{2}-h_1\right)} and \mathrm{ \left(\frac{H}{2}+h_2\right)}. The horizontal ranges will be equal if

\mathrm{ 2 \sqrt{\left(\frac{H}{2}+h_1\right)\left(\frac{H}{2}-h_1\right)}=2 \sqrt{\left(\frac{H}{2}+h_2\right)\left(\frac{H}{2}-h_2\right)} }

which gives \mathrm{ h_1=h_2}.

Hence the correct choice is (a).

Posted by

Ritika Harsh

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