Near the Earth’s surface, g changes with both altitude h and depth d.
(i) Starting from the exact expressions gh=(R+h)2GM and gd=g(1−Rd), obtain the first-order rates of change dhdgh and dddgd evaluated at h=0 and d=0 respectively.
(ii) Hence find the ratio of the magnitudes of these two rates and interpret its physical meaning.
(iii) On the same set of axes draw neat, labelled qualitative graphs of g versus the fractional quantities h/R (for altitude) and d/R (for depth) up to 0.3. Mark the linear segments and the region where deviation from linearity begins for each curve.