Even if the earth were perfectly spherical in shape the weight of a body would vary with latitude. Why?

The value of acceleration due to gravity considering the rotation of the earth is, \[g’=g-\omega^2R\cos^2\theta\]

If earth was perfectly spherical in shape, then $R$ is constant. But from location to location, the latitude $(\theta)$ of earth is different. So, $g’$ will vary from minimum value at the equator $(\theta=0°)$ to the maximum value at poles $(\theta=90°)$.

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