The acceleration due to gravity on the earth's surface at the poles is $g$ and angular velocity of the earth about the axis passing through the pole is $\omega$. An object is weighed at the equator and at a height $h$ above the poles by using a spring balance. If the weights are found to be same, then $h$ is: ($h \ll R$, where $R$ is the radius of the earth)\\
(1) $\frac{R^2\omega^2}{2g}$\\
(2) $\frac{R^2\omega^2}{g}$\\
(3) $\frac{R^2\omega^2}{4g}$\\
(4) $\frac{R^2\omega^2}{8g}$