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KVPY Sample Paper KVPY Stream-SX Model Paper-24

  • question_answer
    Water flows into a large tank with flat bottom at the rate of \[{{10}^{-4}}{{m}^{3}}{{s}^{-1}}.\] Water is also leaking out of area 1 \[C{{m}^{2}}\] at its bottom. If the height of the water in the tank remains steady, then this height is:

    A) 5.1 cm

    B) 1.7 cm

    C) 4 cm    

    D) 2.9 cm

    Correct Answer: A

    Solution :

    \[\frac{dV}{dt}=\phi -a\sqrt{2gh}=0\](for maximum height)
    \[h=\frac{{{\phi }^{2}}}{2g{{a}^{2}}}=\frac{{{10}^{-8}}}{2\times 9.8\times {{10}^{-8}}}=5.1cm.\]


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