KVPY Sample Paper KVPY Stream-SX Model Paper-21

  • question_answer
    Two bar magnets of the same mass, same length and breadth but having magnetic moments M and 2M are joined together pole for pole and suspended by a string. The time period of assembly in a magnetic field of strength H is 3 seconds. If now the polarity of one of the magnets is reversed and the combination is again made to oscillate in the same field, the time period of oscillation is :

    A) \[\sqrt{3}\,\,\,\sec \]

    B) \[3\sqrt{3}\,\,\,\sec \]

    C)  3 sec

    D) 6 sec

    Correct Answer: B

    Solution :

    Time period of magnet oscillating in uniform \[B=T-2\pi \sqrt{\frac{I}{MB}}\]
    M = Magnetic moment \[T\propto \frac{1}{\sqrt{M}}\]
    \[{{M}_{net}}\] of the combination = \[M+2M=3M\]
    \[{{T}_{1}}\propto \frac{1}{\sqrt{3M}}\]
    \[{{M}_{net}}\] of the combination \[=2M-M=M\]
    \[{{T}_{2}}\propto \frac{1}{\sqrt{M}}\]
    \[\frac{{{T}_{1}}}{{{T}_{2}}}=\sqrt{\frac{M}{3M}}\]\[\Rightarrow {{T}_{2}}=\sqrt{3}\,\,{{T}_{1}}\]

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