I've seen an experiment where a closed book with a piece of paper lying on its cover is dropped a short distance (the piece of paper is smaller than the book; the book's cover is parallel to the Earth's surface). Both book and paper fall together and this is supposed to demonstrate that all objects (regardless of their mass) experience the same acceleration when in a state of free fall. But are there other reasons why the book and paper don't separate during their fall? Would not air pressure keep the paper pressed against the book's cover? I guess I'm thinking about the experiment where you can break a ruler under a newspaper because of air pressure.
The actual experiment was performed with a stone and a feather in two vacuum tubes of sane length. It was demonstrated that both the stone and the feather fall the same distance in the same time, which shows that the time if fall is independent of the masses of the body.
In the experiment you stated, there may be chances of the book and the paper separating due to air interaction and upthrust. It has to be performed in a place where air is absolutely static, otherwise there may be chances of both separating.
One may argue that atmospheric pressure keeps the book and the paper together. The argument is completely valid when you look at the experiment solely. But in the light of the actual experiment that I stated above, this argument is ignored, and it is generally taken that air pressure doesn't act on the two bodies.
Would not air pressure keep the paper pressed against the book's cover?
To an extent, possibly.
This is not the main reason why it is done though; although it does relate to your newspaper-ruler example.
The reason would be to minimize the effects of air drag on the piece of paper. Although all objects influenced the same by gravity; they react differently with the air. A piece of paper would fall a lot slower than the book if they were both exposed to air drag. Instead; the piece of paper avoids the drag by travelling in the streamline of the book.
Realistically, if the piece of paper were to fall slower than the book under the influence of gravity (due to lower mass) then even with the air pressure, it should still slowly separate from the book. (the reason the ruler breaks in the newspaper experiment is because you are trying to act against the pressure very quickly).
Either way; this isn't really a great experiment to demonstrate how different masses react the same to gravitational force. Both the book and the paper have very large areas; therefore the drag force is substantial. To eliminate the drag force they set up the experiment in a way that pressure differences could keep the paper and the book falling with similar speeds, even if gravity was acting unevenly.
Really, this test should be done in a vacuum to eliminate this source of potential error. It's a good sign that you can recognize this error in the experiment. Noticing details like this is important when designing good experiments.