In a vibration magnetometer, the time period of a bar magnet oscillating in horizontal component of earth's magnetic field is $2$ $sec$. When a magnet is brought near and parallel to it, the time period reduces to $1 $ $sec$. The ratio $H/F $ of the horizontal component $H$  and the field $F$ due to magnet will be

  • A

    $3$

  • B

    $1/3$

  • C

    $\sqrt 3 $

  • D

    $1/\sqrt 3 $

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  • [AIIMS 2006]