JEE Main & Advanced Sample Paper JEE Main Sample Paper-43

  • question_answer
    A tank is filled with water of density \[1\text{ }g/c{{m}^{3}}\] and oil of density \[0.9\text{ }g/c{{m}^{3}}\] . The height of water layer is 100 cm and of the oil layer is 400 cm. lf \[g=980\text{ }cm/{{s}^{2}}\] , then the velocity of efflux from an opening in the bottom of the tank is

    A)  \[\sqrt{900\times 980}\,\,cm/s\]         

    B)  \[\sqrt{100\times 980}\,\,cm/s\]

    C)  \[\sqrt{920\times 980}\,\,cm/s\]         

    D)  \[\sqrt{950\times 980}\,\,cm/s\]

    Correct Answer: C

    Solution :

     Let, \[\Rightarrow \] and \[v'\frac{v}{\sqrt{2}}\] be the densities of water and oil, then the pressure at the bottom of the tank \[={{h}_{w}}{{d}_{w}}g+{{h}_{o}}{{d}_{o}}g\] Let, this pressure be equivalent to pressure due to water of height h. Then, \[E=\frac{1}{2}mv{{'}^{2}}+\frac{1}{2}mv{{'}^{2}}+\frac{1}{2}(2m){{v}^{2}}\] \[=mv{{'}^{2}}+m{{v}^{2}}\]   \[\Rightarrow \] \[m{{\left( \frac{v}{\sqrt{2}} \right)}^{2}}+m{{v}^{2}}=\frac{3}{2}m{{v}^{2}}\] \[{{T}_{1}}-{{T}_{2}}=12a\] According to Tori celli's theorem, \[{{T}_{2}}=3a\] \[{{T}_{2}}\]

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