Earth is assumed to be a sphere of radius \(R\). If ' \(\mathrm{g}_\phi\) ' is value of effective acceleration due to gravity at latitude \(30^{\circ}\) and ' \(\mathrm{g}\) ' is the value at equator, then the value of \(\left|g-g_\phi\right|\) is \((\omega\) is angular velocity of rotation of earth, \(\cos 30^{\circ}=\frac{\sqrt{3}}{2}\) )

The formula for acceleration due to gravity at certain latitude is given as
\(\mathrm{g}_\phi=\mathrm{g}_{\text {surface }}-\mathrm{R} \omega^2 \cos ^2 \phi\)
At equator, \(\phi=0^{\circ}\)
\(\therefore \quad \mathrm{g}=\mathrm{g}_{\text {surface }}-\mathrm{R} \omega^2 \cos 0^{\circ}=\mathrm{g}_{\text {surface }}-\mathrm{R} \omega^2... (i)\)
At \(\phi=30^{\circ}\)
\(\mathrm{g}_\phi=\mathrm{R} \omega^2 \cos 30^{\circ}=\mathrm{g}_{\text {surface }}-\frac{3 \mathrm{R} \omega^2}{4}... (ii)\)
\(\therefore \quad\left|\mathrm{g}-\mathrm{g}_\phi\right|=\left(\mathrm{g}_{\text {surfince }}-R \omega^2\right)-\left(\mathrm{g}_{\text {surface }}-\frac{3 \mathrm{R} \omega^2}{4}\right)\) \(... [ From (i) and (ii)]\)
\( \therefore \quad\left|\mathrm{g}-\mathrm{g}_\phi^{-}\right|=R \omega^2\left(1-\frac{3}{4}\right) \)
\( \therefore \quad\left|\mathrm{g}_\phi-\mathrm{g}\right|=\frac{\mathrm{R} \omega^2}{4}\)