NEET Sample Paper NEET Sample Test Paper-32

  • question_answer Two discs of moment of inertia \[{{I}_{1}}\] and \[{{I}_{2}}\] are rotated about their geometrical axis with angular velocity \[{{\omega }_{1}}\]and \[{{\omega }_{2}}\] respectively. If the two discs are joint face to face coinciding their axes, then the kinetic energy of system:

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

    B)  \[\frac{1}{2}\,({{I}_{1}}+{{I}_{2}})\,({{\omega }_{1}}+{{\omega }_{2}})\]

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

    D)  \[\frac{1}{16}\,({{I}_{1}}+{{I}_{2}})\,{{({{\omega }_{1}}+{{\omega }_{2}})}^{2}}\]

    Correct Answer: C

    Solution :

    From the law of conservation of Angular momentum \[(L)={{I}_{1}}{{\omega }_{1}}+{{I}_{2}}{{\omega }_{2}}=({{I}_{1}}+{{I}_{2}})\omega \] Rotational kinetic energy \[=\frac{1}{2}\frac{{{L}^{2}}}{({{I}_{1}}+{{I}_{2}})}\] \[=\frac{1}{2}\frac{{{({{I}_{1}}{{\omega }_{1}}+{{I}_{2}}{{\omega }_{2}})}^{2}}}{({{I}_{1}}+{{I}_{2}})}\]

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