Common knowledge can be tricky. If someone asked you to, without thinking, answer which would fall first on the surface of the Moon, a coin or a feather, you’d probably answer “coin”. If you could put the Empire State Building 100 metres above the Moon surface next to a feather, common knowledge would make it hard for you to imagine them both touching the surface at the same time after you dropped them simultaneously. Yet, that is exactly what would happen!
A lot of people know that Apollo 15 astronaut, David Scott, dropped a hammer and a falcon feather from his hands while being on the Moon to test Galileo’s theory that they would touch the surface at the same time. And indeed they did!
Lack of atmosphere on the Moon also means no friction between the air molecules and the dropping object like it is case here on Earth, so the friction between non-existent atmosphere and the feather is the same as the friction between atmosphere and some heavy object like coin, hammer or even building = zero.
Still, many people ask the question why, regardless of the lack of friction, building isn’t attracted more by the Moon's gravity having in mind that it is heavier and that the gravity has more effect the heavier the object.
Here comes the math part of the answer. Gravitational force is indeed proportional to the mass of the object, but the acceleration is not affected by the mass of the object. “g” is gravitational acceleration on Earth and it has value 9.81m/s^2. Gravitational acceleration on the Moon has value of 1.622 m/s^2 (only 16.6% of “g” on Earth). If we use good ol’ Newton’s formula where force equals mass times acceleration (F = ma), we get that the gravitational force “G” is equal to the mass of the object “m” multiplied by the acceleration, on Earth “g”, on the Moon 0.166 times “g” (16.6% of “g”) - G = m x 0.166 x g.
If you increase the mass of an object in the formula above, gravitational force “G” will indeed increase, but acceleration “g” will not. However, while the gravitational force is greater for a building than that for a feather, the inertia for the building is also proportionally higher so in the end they cancel out. Inertia is the resistance to the change of motion of a physical object and it rises with the mass. The more massive the object, the more resistant it is to any change in its speed and direction. Yes, the coin is attracted to the Moon with more force than the feather, but it also resists more to the change in its motion.
Hope that clears it up for you!