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Haryana PMT Haryana PMT Solved Paper-2005

  • question_answer
    The angular speed of a body changes from \[{{\omega }_{1}}\] to \[{{\omega }_{2}}\] without applying a torque, but due to change in moment of inertia. The ratio of radii of gyration in the two cases is :

    A)  \[\sqrt{{{\omega }_{1}}}:\sqrt{{{\omega }_{2}}}\]                           

    B)  \[\sqrt{{{\omega }_{2}}}:\sqrt{{{\omega }_{1}}}\]

    C)  \[{{\omega }_{2}}:{{\omega }_{1}}\]                                     

    D)  \[{{\omega }_{1}}:{{\omega }_{2}}\]

    Correct Answer: C

    Solution :

                    In the absence of external torque \[{{I}_{1}}{{\omega }_{1}}={{I}_{2}}{{\omega }_{2}}\]  or \[MK_{1}^{2}{{\omega }_{1}}=MK_{2}^{2}{{\omega }_{2}}\] \[\therefore \]  \[\frac{{{K}_{1}}}{{{K}_{2}}}=\sqrt{\left( \frac{{{\omega }_{2}}}{{{\omega }_{1}}} \right)}\]


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