Fluid Mechanics

JEE Main level, single correct, medium

85 of 192

Question 85 of 192

In a cylindrical water tank, there are two small holes AA and BB on the wall at a depth of h1h_1, from the surface of water and at a height of h2h_2 from the bottom of water tank. Surface of water is at height of h2h_2 from the bottom of water tank. Surface of water is at heigh HH from the bottom of water tank. Water coming out from both holes strikes the ground at the same point SS. Find the ratio of h1h_1 and h2h_2

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Answer: (A) Depends on HH

Range is same for both holes
∴2(H−h1)h1=2(H−h2)h2\therefore 2 \sqrt{\left(\mathrm{H}-h_1\right) h_1}=2 \sqrt{\left(\mathrm{H}-h_2\right) h_2}
Squaring both sides,
4(H−h1)h1=4(H−h2)h2Hh1−h12=Hh2−h22\begin{aligned} & 4\left(H-h_1\right) \mathrm{h}_1=4\left(H-h_2\right) h_2 \\ & H h_1-h_1^2=H h_2-h_2^2 \end{aligned}
On solving we get,
H=h1+h2H=h_1+h_2
Hence, the ratio of h1h2\frac{h_1}{h_2} depends on HH.

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