If a body is dropped from the same height once in the equator and then in the polar region, in which place will it fall faster?

We all know that,

g = (G.M)/R2

∝ 1/R2

From this, we conclude g is inversely proportional to the square of the radius of any heavenly body. In the equator, the radius is longer than in the pole. If the radius decreases, the g increases. So, there is a higher g in the pole than at the equator. Therefore, the body will fall faster in pole if it is dropped from equal height at the equator and the pole.