AIIMS AIIMS Solved Paper-2008

  • question_answer
    A smooth block is released at rest on a 45° incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is     

    A)  \[^{66}Cu,\]                     

    B)  \[7\frac{1}{2}\]

    C)  \[{{\mu }_{k}}=1-\frac{1}{{{n}^{2}}}\]                   

    D)  \[{{\mu }_{k}}=\sqrt{1-\frac{1}{{{n}^{2}}}}\]]

    Correct Answer: A

    Solution :

    When friction is absent              \[{{R}^{2}}\] \[{{R}_{1}}\]    \[{{R}_{2}}\]                 ?..(i) When friction is present \[({{R}_{2}}>{{R}_{1}})\] \[{{R}_{2}}\]   \[R=\frac{{{R}_{2}}\times ({{R}_{1}}+{{R}_{2}})}{({{R}_{2}}-{{R}_{1}})}\]                  ?..(ii) From Eqs. (i) and (ii) \[R={{R}_{2}}-{{R}_{1}}\] or   \[R=\frac{{{R}_{1}}{{R}_{2}}}{({{R}_{1}}+{{R}_{2}})}\]        (\[R=\frac{{{R}_{1}}{{R}_{2}}}{({{R}_{2}}-{{R}_{1}})}\]  \[{{\sin }^{2}}(\omega t)\]0) or   \[2\pi /\omega \] or   \[\pi /\omega \] or \[2\pi /\omega \] or     \[\pi /\omega \] or   \[\frac{4}{3}\]          


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