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KVPY Sample Paper KVPY Stream-SX Model Paper-11

  • question_answer
    A light cylindrical vessel is kept on a horizontal surface. Its base area is A.A hole of cross sectional area a is made just at its bottom side. The minimum coefficient of friction necessary for sliding of the vessel due to the impact force of the emerging liquid is \[~\left( a<<A \right):\]

    A) Varying            

    B) \[\frac{a}{A}\]

    C) \[\frac{2a}{A}\]

    D) none of these

    Correct Answer: C

    Solution :

    the velocity of the .liquid id given as  \[v=\sqrt{2gy}\]
    \[\therefore \]the impact  force of the emerging liquid  on the vessel+ liquid content is equal to \[F=v\frac{dm}{dt}=vapv=ap{{v}^{2}}\]
    \[\Rightarrow F=ap{{\left( \sqrt{2gh} \right)}^{2}}=2apgy\]
    The force of friction, \[f=F=2apgy\]
    \[\Rightarrow \mu N=2a\rho gy\Rightarrow \mu \left( A\rho gy \right)=2a\rho gy\] \[\Rightarrow \mu =\frac{2a}{A}\]


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