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

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$π \sqrt{\frac{R}{g}}$

$\frac{π}{2} \sqrt{\frac{R}{g}}$

$\frac{π}{3} \sqrt{\frac{R}{g}}$

$2 π \sqrt{\frac{R}{g}}$

answer is A.

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Detailed Solution

$g' = g - R_{e} ω^{2} \cos^{2} λ, O = g - R_{e} ω^{2} \cos^{2} λ, ω = \sqrt{\frac{g}{R_{e} \cos^{2} λ}} = \sqrt{\frac{g}{R_{e} (\frac{1}{4})}} = \sqrt{\frac{4 g}{R_{e}}} T = \frac{2 π}{ω}$

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