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JEE Main & Advanced JEE Main Paper (Held On 26 May 2012)

  • question_answer
    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 height 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 \[{{h}_{2}}\]   JEE Main Online Paper (Held On 26-May-2012)  

    A) Depends on H

    B) 1:1

    C) 2:2                                         

    D) 1:2

    Correct Answer: A

    Solution :

    Range is same for both holes \[\therefore \]\[2\sqrt{(H-{{h}_{1}}){{h}_{1}}}=2\sqrt{(H-{{h}_{2}}){{h}_{2}}}\] 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 \[\frac{{{h}_{1}}}{{{h}_{2}}}\]depend  on H.


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