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At what rate should the earth rotate so ...

At what rate should the earth rotate so that the apparent g at the equator becomes zero? What will be the length of the day in this situation?

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The apparent ` g = g_(0) - omega^(2) R = 0 `
` rArr " " omega = sqrt((g_(0))/R ) = sqrt((9.8 "ms"^(-2))/(6.4 xx 10^(6)m) ) = 1.237 xx10^(-3) ` rad/s
The length of the day = Time period of rotation of the Earth
` = (2pi)/omega = 2pisqrt((R)/(g_(0))) = 1.41` hour .
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