JEE Main & Advanced Physics Fluid Mechanics, Surface Tension & Viscosity / द्रव यांत्रिकी, भूतल तनाव और चिपचिपापन Question Bank Self Evaluation Test - Mechanical Properties of Fluids

  • question_answer
    . Water is filled in a cylindrical container to a height of 3m. The ratio of the cross-sectional area of the orifice and the beaker is 0.1. The square of the speed of the liquid coming out from the orifice is (\[g=10m/{{s}^{2}}\])

    A) \[50{{m}^{2}}/{{s}^{2}}\]

    B) \[50.5{{m}^{2}}/{{s}^{2}}\]

    C) \[51{{m}^{2}}/{{s}^{2}}\]

    D) \[52{{m}^{2}}/{{s}^{2}}\]

    Correct Answer: A

    Solution :

    [a] If \[{{v}_{2}}\]is the required speed then \[{{A}_{1}}{{v}_{1}}={{A}_{2}}{{v}_{2}}\] or \[{{v}_{1}}=\frac{{{A}_{2}}}{{{A}_{1}}}{{v}_{2}}=0.1{{v}_{2}}\]                     ...(i) From Bernoulli's equation, we have \[Pa+\frac{1}{2}\rho v_{1}^{2}+\rho g(3-0.525)=Pa+\frac{1}{2}\rho v_{2}^{2}+0\]                             ...(ii) After solving above equations, we get \[v_{2}^{2}=50{{m}^{2}}/{{s}^{2}}\]


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