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Punjab Medical Punjab - MET Solved Paper-2010

  • question_answer
    A ball of mass\[m\]and density\[\rho \]is immersed in a liquid of density\[\rho \]at a depth\[h\]and released. To what height will the ball jump up above the surface of liquid? (Neglect the resistance of water and air)

    A) \[h\]                                     

    B) \[\frac{h}{2}\]

    C) \[3h\]                                   

    D) \[2h\]

    Correct Answer: D

    Solution :

    Volume of ball\[=m/\rho \]Acceleration of the ball inside the liquid,                 \[a=\frac{{{F}_{net}}}{m}=\frac{upthrust-weight}{m}\] \[a=\frac{\left( \frac{m}{\rho } \right)(3\rho )g-mg}{m}=2g,\]upwards Velocity of the ball on reaching the surface,                 \[v=\sqrt{2ah}=\sqrt{4gh}\] The ball will jump to a height                 \[H=\frac{{{v}^{2}}}{2g}=\frac{4gh}{2g}=2h\]


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