Consider four locations measured along the same vertical line through a point on Earth’s surface:
A: altitude h1=20km above the surface
B: altitude h2=30km above the surface
C: depth d1=20km below the surface
D: depth d2=30km below the surface
Assume each distance is much smaller than Earth’s radius R.
Answer the following.
(i) On the same set of axes, sketch qualitative graphs of g versus displacement x (where x is positive upward and negative downward) for the ranges shown, labelling the slopes clearly.
(ii) Using the sketch or otherwise, arrange the four locations A, B, C and D in ascending order of the weight of an identical body placed at each position.
(iii) Justify your ranking with suitable calculations, keeping only first-order terms in ∣x∣/R.
(iv) Discuss briefly how the ranking would be affected if the displacements were not small compared with Earth’s radius.