If the apparent weight of the bodies at the equator is to be zero, then the earth should rotate with

Question

If the apparent weight of the bodies at the equator is to be zero, then the earth should rotate with angular velocity

Professor PC Thomas Classes · Answer

Apparent acceleration due to gravity at latitude $\lambda$ is $g' = g - \omega^2 R \cos^2\lambda$. At the equator, latitude $\lambda = 0^\circ$, so $g' = g - \omega^2 R$. For apparent weight to be zero, $g' = 0 \implies g - \omega^2 R = 0 \implies \omega = \sqrt{g/R}$.