The rotation of the earth having $R$ radius about its axis speeds up to a value such that  a man at latitude angle $60^o$ feels weightlessness. The duration of the day in such a  case is.

  • A

    $2 \pi \sqrt{\frac{R}{g}}$

  • B

    $ \pi \sqrt{\frac{R}{g}}$

  • C

    $2 \pi \sqrt{\frac{g}{R}}$

  • D

    $4 \pi \sqrt{\frac{R}{g}}$

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