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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2011

  • question_answer
        The cylindrical tube of a spray pump has a cross-section of\[8\text{ }c{{m}^{2}},\] are end of which has 45 fine holes each of area\[{{10}^{-8}}{{m}^{2}}\]. If the liquid flows inside the tube with a speed of 0.15 m \[mi{{n}^{-1}},\]the speed with which the liquid is ejected through the holes is

    A)  \[50\,m{{s}^{-1}}\]

    B)  \[5\,m{{s}^{-1}}\]

    C)  \[0.05\,m{{s}^{-1}}\]

    D)  \[0.5\,m{{s}^{-1}}\]

    Correct Answer: B

    Solution :

                    According to equation of continuity, \[Area\text{ (}a)\,\times Velocity\,\text{(}v)=Constant.\] For tube, \[8\times {{10}^{-4}}\times \left( \frac{0.15}{60} \right)={{a}_{1}}{{v}_{1}}\] For holes, \[(40\times {{10}^{-8}})\times v={{a}_{2}}{{v}_{2}}\] \[\therefore \]  \[{{a}_{2}}{{v}_{2}}={{a}_{1}}{{v}_{1}}\] \[40\times {{10}^{-8}}\times v=\frac{8\times {{10}^{-4}}\times 0.15}{60}\]                 \[v=\frac{8\times 15}{4\times 6}=5\,m{{s}^{-1}}\]


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