RAJASTHAN ­ PET Rajasthan PET Solved Paper-2005

  • question_answer
    A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity \[\omega \]. Two objects each of mass m, are kept gently to the opposite ends of two perpendicular diameter of the ring. The angular velocity of the ring will be

    A)  \[\frac{M\omega }{2m}\]

    B)  \[\frac{2M\omega }{M}\]

    C)  \[\frac{(M+2m)}{M}\omega \]

    D)  \[\left( \frac{M\omega }{M+2\omega } \right)\]

    Correct Answer: D

    Solution :

     \[{{I}_{1}}{{\omega }_{1}}={{I}_{2}}{{\omega }_{2}}\] \[\frac{M{{R}^{2}}}{2}\omega =\frac{1}{2}(M+2m){{R}^{2}}{{\omega }^{2}}\] \[{{\omega }_{2}}=\left( \frac{M\omega }{M+2m} \right)\]


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