A body of mass m is taken to a small height h above the Earth’s surface and then to an equal depth d below the surface (h,d≪R, where R is the Earth’s radius).
(i) Derive an expression for the fractional change in the acceleration due to gravity at height h in terms of h and R.
(ii) Using a similar method, derive the fractional change in the acceleration due to gravity at depth d.
(iii) For h=d=500m and R=6.4×106m, calculate the percentage change in g in each case, retaining two significant figures.
(iv) Comment on which change (at height or at depth) is numerically larger and give a physical reason for the difference.