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BHU PMT BHU PMT Solved Paper-2002

  • question_answer
    The angular speed of a body changes from \[\mu \,\,\cos \,\,a\] to \[g\,\,\sin \,\,a\] without applying a torque but due to change in its moment of inertia. The ratio of radii of gyration in the two cases is:              [BHU PMT-2002]

    A)                  \[Zero\]                                             

    B)                  \[0.125\,\,kg\]

    C)                  \[0.5\,\,kg\]                     

    D)                  \[0.25\,\,kg\]

    Correct Answer: D

    Solution :

                     Key Idea: In the absence of external torque angular momentum is conserved.                 The radius of gyration \[\text{mg sin a}-{{f}_{\text{k}}}=ma\] of  a body about a given line is defined as                                                 \[{{f}_{\text{k}}}\]                 Where, \[{{f}_{K}}=\mu \,R=\mu \,\,mg\,\,\cos \,\,a\] is its moment of inertia and \[\therefore \] is its total mass.                                                 \[mg\,\,\sin \,\,a-\mu mg\,\,\cos \,\,a=ma\]                                                 \[\Rightarrow \]                 \[a=g\left( \sin \,\,a-\mu \,\,\cos \,\,a \right)\]                 \[N\]                 \[N\]                     \[35\mu A\]


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