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NEET Sample Paper NEET Sample Test Paper-68

  • question_answer
    A horizontal turn table in the form of a disc of radius r carries a gun at G and rotates with angular velocity \[{{\omega }_{0}}\] about a vertical axis passing through the centre O.  The increase in angular velocity of the system if the gum fires a bullet of mass m with a tangential velocity \[\nu \] with respect to the gum is (moment of inertia of gun + table about O is \[{{I}_{0}}\])                                               

    A) \[\frac{m\nu r}{{{I}_{0}}+m{{r}^{2}}}\]

    B)               \[\frac{2m\nu r}{{{I}_{0}}}\]

    C) \[\frac{\nu }{2r}\]                                  

    D) \[\frac{m\nu r}{2{{I}_{0}}}\]  

    Correct Answer: A

    Solution :

    Given that \[{{I}_{0}}\] is the moment of inertia of table and gun and m the mass of bullet.                Initial angular momentum of system about centre \[{{\operatorname{L}}_{i}} =\left( {{I}_{0}} + m{{r}^{2}} \right){{\omega }_{0}}\] Let co be the angular velocity of table after the bullet is fired. Final angular momentum    \[{{L}_{f}}={{I}_{0}}\omega  -\,\,m(\nu  - r\omega )r\] where \[(\nu -r\omega )\] is absolute velocity of bullet to the right.                                  Equating (i) and (ii), we get \[(\omega -{{\omega }_{0}})=\frac{m\nu r}{{{I}_{0}}+m{{r}^{2}}}\]


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