Explanation

(a) $As\ \ g^{'} = g - \omega^{2}R\ \cos^{2}\ \lambda$
The latitude at point on the surface of the earth is defined as the angle, which the line joining that point to the centre of earth makes with equatorial plane. It is denoted by λ. For the poles $\lambda = 90{^\circ}$ and for equator $\lambda = 0{^\circ}$.
(i) Substituting $\lambda = 90{^\circ}\ $in the above expression, we get
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ g_{pole} = g - \omega^{2}R\cos^{2}\ 90{^\circ}$
${\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ g}_{pole} = g$
$ie,$ there is no effect of rotational motion of the earth on the value of $g$ at the poles.
(ii) Substituting $\lambda = 0{^\circ}\ $in the above expression, we get
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ g_{equator} = g - \omega^{2}R\cos^{2}\ 0{^\circ}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ g_{equator} = g - \omega^{2}R$
$ie,\ $the effect of rotation of the earth on the value of $g$ at the equator is maximum.