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CMC Medical CMC-Medical VELLORE Solved Paper-2015

  • question_answer
    Water stands at depth \[H\]H in a large open tank whose side walls are vertical are shown in the figure given below. If hole is made in one of the walls at a depth of \[h\] below the water surface, the emerging steam will strike the floor at a distance \[d\]is given by

    A)  \[2H(H-h)\]                       

    B)  \[\sqrt{h\,(H-h)}\]

    C)  \[\sqrt{h\,(H+h)}\]                        

    D)  \[12\sqrt{h\,(H-h)}\]

    E)  \[\frac{2H}{h}\]

    Correct Answer: D

    Solution :

                    Let v be the velocity at point P of water while ejected, then \[\frac{1}{2}\rho {{v}^{2}}=\rho gh\] \[v=\sqrt{2gh}\] If emerging water will strike the floor after time t, then \[H-h=\frac{1}{2}g{{t}^{2}}\] \[\Rightarrow \]               \[t=\sqrt{\frac{2\,(H-h)}{g}}\] The distance covered, d = vt \[\Rightarrow \]               \[d=2\,\sqrt{h\,(H-h)}\]


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