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WB JEE Medical WB JEE Medical Solved Paper-2006

  • question_answer
    A cylinder of height 20 m is completely filled with water. The velocity of efflux of water (in \[\text{m}{{\text{s}}^{-1}}\]through a hole on the side wall of the cylinder near its bottom, is :

    A)  10                                         

    B)  20

    C)  25.5                                      

    D)  5

    Correct Answer: B

    Solution :

                     Let \[{{P}_{0}}\]is the atmospheric pressure, \[\rho \]thedensity of liquid and v the velocity at whichwater is coming out. Apply the Bernoullistheorem just inside and outside the hole. \[{{P}_{\text{inside}}}+\rho gh+0={{P}_{\text{outside}}}+\frac{\rho {{v}^{2}}}{2}\] \[\Rightarrow \]               \[{{P}_{0}}+\rho gh={{P}_{0}}+\frac{\rho {{v}^{2}}}{2}\] \[\Rightarrow \]               \[v=\sqrt{2gh}=\sqrt{2\times 10\times 20}=20\,m/s\]


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