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NEET Sample Paper NEET Sample Test Paper-40

  • question_answer
      A circular disk of moment of inertia \[{{I}_{t}}\] is rotating in a horizontal plane about its symmetry axis, with a constant angular speed\[{{\omega }_{i}}\]. Another disk of moment of inertia \[{{I}_{b}}\] is dropped coaxially onto the rotating disk, initially the second disk has zero angular speed. Eventually both the disks rotate with a constant angular speed \[{{\omega }_{f}}.\]The energy lost by the initially rotating disc due to friction is:

    A) \[\frac{1}{2}\frac{I_{b}^{2}}{({{I}_{t}}+{{I}_{b}})}\omega _{i}^{2}\]

    B) \[\frac{1}{2}\frac{I_{t}^{2}}{({{I}_{t}}+{{I}_{b}})}\omega _{i}^{2}\]

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

    D) \[\frac{1}{2}\frac{{{I}_{b}}{{I}_{t}}}{({{I}_{t}}+{{I}_{b}})}\omega _{i}^{2}\] 

    Correct Answer: D

    Solution :

     Loss of energy, \[\Delta E={{K}_{initial}}-{{K}_{final}}=\frac{1}{2}{{I}_{1}}\omega _{i}^{2}\]\[-\frac{1}{2}\frac{I_{t}^{2}\omega _{i}^{2}}{({{I}_{t}}+{{I}_{b}})}\] \[=\frac{1}{2}\frac{{{I}_{b}}{{I}_{t}}\omega _{i}^{2}}{({{I}_{t}}+{{I}_{b}})}\]


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