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WB JEE Medical WB JEE Medical Solved Paper-2006

  • question_answer
    A liquid flows through a pipe of non-uniform cross-section. If \[{{\text{A}}_{\text{1}}}\]and \[{{\text{A}}_{2}}\]arc the cross-sectional areas of the pipe at two points, the ratio of velocities of the liquid at these points will be :

    A)  \[{{A}_{1}}{{A}_{2}}\]                   

    B)  \[\frac{{{A}_{1}}}{{{A}_{2}}}\]

    C)  \[\frac{{{A}_{2}}}{{{A}_{1}}}\]  

    D)  \[\frac{1}{{{A}_{1}}{{A}_{2}}}\]

    Correct Answer: C

    Solution :

                     Volume of liquid flowing at first point \[=A{{ & }_{1}}{{v}_{1}}\]Similarly, volume of liquid flowing at second point \[=A{{ & }_{2}}{{v}_{2}}\] From equation of continuity, \[{{A}_{1}}{{v}_{1}}={{A}_{2}}{{v}_{2}}\]                 or                            \[\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{{{A}_{2}}}{{{A}_{1}}}\]


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