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JCECE Medical JCECE Medical Solved Paper-2013

  • question_answer
    Equal volume of two immiscible liquids of densities \[\rho \]and \[2\rho \]are filled in a vessel as shown in figure. Two small holes are made at depth \[\frac{h}{2}\]and \[\frac{3h}{2}\] from the surface of lighter liquid. If \[{{\upsilon }_{1}}\]and \[{{\upsilon }_{2}}\]are the velocities of efflux at these two holes, then \[{{\upsilon }_{1}}/{{\upsilon }_{2}}\]will be

    A) \[\frac{1}{\sqrt{2}}\]

    B)  \[\frac{1}{2\sqrt{2}}\]

    C)  \[\frac{1}{2}\]

    D)   \[\frac{1}{4}\]

    Correct Answer: A

    Solution :

     We have\[{{v}_{1}}=\sqrt{2gh(h/2)}=\sqrt{gh}\] ?(i) and by using Bernoullis theorem \[\rho \,gh+2\rho g\left( \frac{h}{2} \right)=\frac{1}{2}(2\rho )v_{2}^{2}\] \[\Rightarrow \] \[{{v}_{2}}=\sqrt{2}gh\] ?(ii) From Eqs. (i).and (ii) \[\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{1}{\sqrt{2}}\]


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