Inspired by Parag Zode

We have that:

$m'a=\frac { GMm' }{ { (R+h) }^{ 2 } } \longrightarrow a=\frac { GM }{ { (R+h) }^{ 2 } }$

We also have that:

$mg=\frac { GMm }{ { R }^{ 2 } } \longrightarrow GM=g{ R }^{ 2 }$

Substituting the second equation in the first:

$a=\frac { g{ R }^{ 2 } }{ { (R+h) }^{ 2 } }$

$\boxed{a=g{ \left( \frac { R }{ R+h } \right) }^{ 2 }}$

Let $a$ be the acceleration due to gravity, $G$ be the gravitational constant and $m$ be the mass of Earth. From the definition of g $g = G\frac{m}{R^2}\Leftrightarrow Gm = gR^2$ and from Newton's law of universal gravitation, $a = G\frac{m}{(R + h)^2}$ Substituting the (right side of the) first equation into the second gives $a = g\frac{R^2}{(R+h)^2} = \boxed{g(\frac{R}{R+h})^2}$

Note that this is not a strictly correct formula, even by pre-relativity standards, as Earth is not a point mass or a perfect sphere of uniform density. It is simply a better approximation.

Now, of course, everyone who's studied even a little about classical mechanics knows this and even remembers the answer without even doing any work. This question is an interesting one because it allows us to use only a little reasoning and eliminate all the other choices. Here's the solution:

The choices leaving the correct one all imply that force of gravity increases with height, which we know does not.