Tides above, and tides below

Suppose $g_\downarrow(h)$ is the acceleration due to gravity at a depth $h$ below Earth's surface, while $g_\uparrow(h)$ is the acceleration due to gravity a height $h$ above Earth's surface. Form the function $f(h) = \frac{g_\downarrow(h)}{g_\uparrow(h)}.$

How does $f(h)$ vary as we move from $h=0$ to $h=R$ ?

Details

• Assume Earth to be a uniform sphere of radius $R$ .

This problem is originally part of set Mechanics problems by Abhishek Sharma . Try more problems here .