The acceleration due to gravity on the earth's surface at the poles is $g$ and the angular velocity of the earth about the axis passing through the poles 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 the same,then $h$ is: ($h << R$,where $R$ is the radius of the earth)

• A
  $\frac{R^{2} \omega^{2}}{8g}$
• B
  $\frac{R^{2} \omega^{2}}{4g}$
• C
  $\frac{R^{2} \omega^{2}}{g}$
• D
  $\frac{R^{2} \omega^{2}}{2g}$