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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2005

  • question_answer
        Initial angular velocity of a circular disc of mass M is\[{{\omega }_{1}}\]. Then two small spheres of mass m are attached gently to two diametrically opposite points on the edge of the disc. What is the final angular velocity of the disc?

    A)  \[\left( \frac{M+m}{M} \right){{\omega }_{1}}\]                             

    B)  \[\left( \frac{M+m}{m} \right){{\omega }_{1}}\]

    C)  \[\left( \frac{M}{M+4m} \right){{\omega }_{1}}\]           

    D)  \[\left( \frac{M}{M+2m} \right){{\omega }_{1}}\]

    Correct Answer: C

    Solution :

                    Conservation of angular momentum gives \[\frac{1}{2}M{{R}^{2}}{{\omega }_{1}}=\left( \frac{1}{2}M{{R}^{2}}+2M{{R}^{2}} \right){{\omega }^{2}}\] \[\Rightarrow \]\[\frac{1}{2}M{{R}^{2}}{{\omega }_{1}}=\frac{1}{2}{{R}^{2}}(M+4m){{\omega }_{2}}\] \[\therefore \]  \[{{\omega }_{2}}=\left( \frac{M}{M+4m} \right){{\omega }_{1}}\]


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