Question

For given values of angular speed and acceleration due to gravity, find the position (latitude) where acceleration due to gravity is
(a) Maximum and (b) Minimum.

Answer 1

(a) Variation of $g$ with latitude is given by
$g^{\prime }=g-R{\omega }^2{\cos }^2\theta$
$g^{\prime }$ will be maximum when ${\cos }^2\theta$ is minimum, i.e. $=0$, or, when $\theta ={90}^{\circ }$
$\Rightarrow g_{max}=g$, at the poles.
(b) $g^{\prime }$ will be minimum when ${\cos }^2\theta$ is maximum
$\Rightarrow$ i.e. $\theta =0$
$g_{min}=g-R{\omega }^2$, at the equator.