Let's imagine a planet that is 5000 km in diameter but has the mass of the Earth. I'd imagine standing on that planet might feel similar to standing on the Earth, because the gravity would be comparable.
However, at smaller and smaller volumes, there would be a greater difference in gravity with a smaller change in distance from the planet's center. Standing on a spherical object only a few meters in diameter with the mass of the Earth, the bottoms of your feet might experience Earth-like gravity, but your head would experience hardly any gravity at all. I'd imagine this would cause some serious health problems.
I imagine that no matter what, there might be some health problems when changing the volume of the Earth-like mass; however, I want to know what the smallest volume could be that has no immediate (no problems for at least a few years) health problems.
How small can a planet or object of Earth-like mass be without being overly dangerous?
Worldbuilding context: I am wondering what the smallest object can be that has Earth-like gravity. It would be interesting to be able to run around the world very quickly.
NOTE: I am only interested in the gravitational affects on the human body, so please ignore any other affects. I don't care about retaining Earth's qualities. The question How small in diameter a planet can be while retaining most of Earth's properties? is asking for much more than my question.