J & K CET Engineering J and K - CET Engineering Solved Paper-2009

  • question_answer \[{{I}_{1}}\] and \[{{I}_{2}}\] are the moments of inertia of two circular discs about their central axes perpendicular to their surfaces. Their angular frequencies of rotation are \[{{\omega }_{1}}\] and \[{{\omega }_{2}}\] respectively. If they are brought into contact face to face with their axes of rotation coinciding with each other, the angular frequency of the composite disc will be

    A)  \[\frac{{{I}_{1}}+{{I}_{2}}}{{{\omega }_{1}}+{{\omega }_{2}}}\]

    B)  \[\frac{{{I}_{2}}{{\omega }_{1}}-{{I}_{1}}{{\omega }_{2}}}{{{I}_{1}}-{{I}_{2}}}\]

    C)  \[\frac{{{I}_{2}}{{\omega }_{1}}+{{I}_{1}}{{\omega }_{2}}}{{{I}_{1}}+{{I}_{2}}}\]

    D)  \[\frac{{{I}_{1}}{{\omega }_{1}}+{{I}_{2}}{{\omega }_{2}}}{{{I}_{1}}+{{I}_{2}}}\]

    Correct Answer: D

    Solution :

    According to conservation of angular momentum \[{{I}_{1}}{{\omega }_{1}}+{{I}_{2}}{{\omega }_{2}}=({{I}_{1}}+{{I}_{2}})\omega \] \[\frac{{{I}_{1}}{{\omega }_{1}}+{{I}_{2}}{{\omega }_{2}}}{({{I}_{1}}+{{I}_{2}})}=\omega \]

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