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NEET Physics Magnetism NEET PYQ-Magnetism

  • question_answer
    Two bar magnets having same geometry with magnetic moments M and 2M, are firstly placed in such a way that their similar poles are on the same side; then its period of oscillation is \[{{T}_{1}}\]. Now the polarity of one of the magnets is reversed, then time period of oscillations will be:                                                                                           [AIPMT 2002]

    A)  \[{{T}_{1}}<{{T}_{2}}\]

    B)                   \[{{T}_{1}}>{{T}_{2}}\]

    C)  \[{{T}_{1}}={{T}_{2}}\]

    D)                   \[{{T}_{2}}=\,\infty \]

    Correct Answer: A

    Solution :

    [a] The time period of bar magnet
                            \[T=2\pi \sqrt{\frac{I}{MH}}\]
                where    M= magnetic moment of magnet
                            I = moment of inertia and   
                H = horizontal component of magnetic field
                When same poles of magnets are placed on same side, then net magnetic moment
                            \[{{M}_{1}}=M+2M=3M\]
                \[\therefore \]      \[T{{ & }_{1}}=2\pi \,\sqrt{\frac{I}{{{M}_{1}}H}}\]
                            \[=2\pi \,\sqrt{\frac{I}{3\,M\,H}}\]                                  ....(i)
                When opposite poles of magnets are placed on same side, then net magnetic moment
                            \[{{M}_{2}}=2MM~=M\]
                \[\therefore \]      \[{{T}_{2}}=2\pi \sqrt{\frac{I}{{{M}_{2}}H}}=2\pi \sqrt{\frac{I}{M\,H}}\]        …(ii)
                From Eqs. (i) and (ii), we observe that
                            \[{{T}_{1}}<{{T}_{2}}\]


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