What force arises from direct physical contact between two objects

Any two objects with mass will be attracted to each other by gravity, which is a force that arises purely from mass. Any mass is possessed of gravity, and any two masses will be drawn toward each other by this force. But note that gravity isn't strong enough to cause, say, a rock to be attracted to a brick wall. They are attracted to each other by their mutual gravity, but that mutual gravity cannot overcome the other forces acting on them. The gravitational forces acting in this case are very small when we look at the "big picture" here.