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JEE Main & Advanced Physics Magnetism Question Bank Self Evaluation Test - Magnetism and Matter

  • question_answer
    The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is 2 s. The magnet is cut along its length into three equal parts and three parts are then placed on each other with their like poles together. The time period of this combination will be    

    A) 2s                    

    B)                    \[2/3s\]

    C)             \[2\sqrt{3\,}s\]

    D)                                \[2/\sqrt{3\,}s\]

    Correct Answer: B

    Solution :

    [b] The moment of inertia of original magnet \[I=\frac{m{{\ell }^{2}}}{12}\] After dividing into three equal parts, \[I'=3(m/3).\frac{{{(\ell /3)}^{2}}}{12}=\frac{I}{9}.\] Also magnetic moment, M' = M Now, \[\frac{T'}{T}=\sqrt{\frac{I'}{I}\times \frac{M}{M'}}\] \[\therefore \,\,\,\,\,\,T'=T\times \sqrt{\frac{I'}{I}}=2\times \sqrt{\frac{I}{9}}=\frac{2}{3}s.\]


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