The acceleration due to gravity at point $P$ having latitude $\lambda$ is given by
$g'=g-R \omega^{2} \cos ^{2} \lambda$
$\Rightarrow M g'=m g-m R \omega^{2} \cos ^{2} \lambda$
At equator: $\lambda=0^{\circ} ; m g^{\prime}=m g-m R \omega^{2}$
At pole: $\lambda=90^{\circ} ; m g'=m g-m R \omega^{2} \cos ^{2} 90^{\circ}$
$\Rightarrow m g'=m g$
That is, weight of the object at poles remains unchanged. Thus, the difference in weight is
$\left(m g-m g'\right)=m R \omega^{2} \cos ^{2} \lambda$
Therefore, the loss in weight depends upon latitude $\lambda$. The effect is maximum at equator.
