The rotation of the earth having \( R \) radius about its axis \( P \) speeds up to a value such...

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The rotation of the earth having \( R \) radius about its axis
\( P \) speeds up to a value such that a man at latitude angle \( 60^{\circ} \) feels

W weightlessness. The duration of the day in such a case is :
(A) \( 2 \pi \sqrt{\frac{R}{g}} \)
(B) \( 4 \pi \sqrt{\frac{R}{g}} \)
(C) \( 2 \pi \sqrt{\frac{g}{R}} \)
(D) \( 4 \pi \sqrt{\frac{g}{R}} \)
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