A body reaches the ground quicker at the poles than at the equator when dropped from the same height. Why?

The value of acceleration due to gravity $(g)$ is more at the poles than at the equator considering both the radius $\left(g=\frac{GM}{R^2}\right)$ and the rotation $(g’=g-\omega^2R\cos^2\theta)$ of the earth.

The time of falling of a body from a certain height $h$ is, \[T=\sqrt{\frac{2h}{g}}\]

Since $g$ is more at poles than equator, the time of falling is less at poles. That’s why, a body reaches the ground quicker at the poles than at the equator when dropped from the same height.

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