In a cylindrical water tank, there are two small holes A and B on the wall at a depth of h 1 , from the surface of water and at a height of h 2 from the bottom of water tank. Surface of water is a

Question

In a cylindrical water tank, there are two small holes $A$ and $B$ on the wall at a depth of $h_{1}$ , from the surface of water and at a height of $h_{2}$ from the bottom of water tank. Surface of water is at height of $h_{2}$ from the bottom of water tank. Surface of water is at heigh $H$ from the bottom of water tank. Water coming out from both holes strikes the ground at the same point $S$ . Find the ratio of $h_{1}$ and $h_{2}$

TestHub · Accepted Answer

Range is same for both holes ∴ 2 ( H − h 1 ​ ) h 1 ​ ​ = 2 ( H − h 2 ​ ) h 2 ​ ​ Squaring both sides, ​ 4 ( H − h 1 ​ ) h 1 ​ = 4 ( H − h 2 ​ ) h 2 ​ H h 1 ​ − h 1 2 ​ = H h 2 ​ − h 2 2 ​ ​ On solving we get, H = h 1 ​ + h 2 ​ Hence, the ratio of h 2 ​ h 1 ​ ​ depends on H .

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