If bodies at the equator of the earth are to be weightless, what should be its time period of rotation ?

If bodies at the equator of the earth are to be weightless, what shoul

1.	If bodies at the equator of the earth are to be weightless, what should be its time period of rotation ?
Answer» SOLUTION :The ACCELERATION due to gravity at LATITUDE `phi` is ` g_phi = g - R omega^2 cos^2 phi` For bodies to be weightless at equator then `g_phi` must be zero.`rArr 0 = g - R omega^2 [ because phi = 0^@]` ` rArr omega^2 = g/R rArr omega = sqrt(g/R) , ` But we know that , `omega = (2pi)/(T) , THEREFORE T = 2pi sqrt(R/g)`