The acceleration due to gravity at the poles and the equator is ${\mathrm{g}}_{\mathrm{p}} \mathrm{and} {\mathrm{g}}_{\mathrm{e}}$ respectively. If the earth is a sphere of radius ${\mathrm{R}}_{\mathrm{E}}$ and rotating about its axis with angular speed
$\mathrm{\omega }$, then ${\mathrm{g}}_{\mathrm{p}}-{\mathrm{g}}_{\mathrm{e}}$ is given by

• A

  $\frac{{\mathrm{\omega }}^2}{{\mathrm{R}}_{\mathrm{E}}}$

• B

  $\frac{{\mathrm{\omega }}^2}{{\displaystyle {\mathrm{R}}_{\mathrm{E}}^2}}$

• C

  ${\mathrm{\omega }}^2{\mathrm{R}}_{\mathrm{E}}^2$

• D

  ${\mathrm{\omega }}^2{\mathrm{R}}_{\mathrm{E}}$