Question

Earth radius is $R$ and spin angular velocity of Earth is $\omega$. At what height above the North pole the acceleration due to gravity will be same as that at the equation? ($g$ is acceleration due to gravity at North pole).

Answer 1

At north pole acceleration due to gravity=$g^{\prime }=g-W^{2}R\cos {}^2\theta$ [W=angular velocity of earth, R=Radius of the earth,$\theta$=latitude]

Here,at north pole ,$\theta =\frac{\pi }{2}\therefore g^{\prime }=g$

At the surface of the Earth in North pole the acceleration due to gravity will be same as that as the equation.