Question

Compare the acceleration due to gravity at height of 16 kilometre above the surface of Earth to that at 32 kilometre below the surface of the earth, given the radius of the earth is 6400 km.

Answer 1

$$\begin{gathered} Accelerationduetogravityatheighthabovethesurfaceofearth: \\ {g}_h=g\left(1-\frac{2h}{R}\right) \\ Accelerationduetogravityatdepthdbelowthesurfaceofearth: \\ {g}_d=g\left(1-\frac{d}{R}\right) \\ Ratio: \\ \frac{g_h}{g_d}=\frac{g\left(1-\frac{2h}{R}\right)}{g\left(1-\frac{d}{R}\right)} \\ =\frac{1-{\displaystyle \frac{2\times 16}{R}}}{1-\frac{32}{R}} \\ \mathbf{}\mathbf{}\mathbf{=}\mathbf{1}\mathbf{:}\mathbf{1} \end{gathered}$$