If I made a tower from earth to twice above the earth atmosphere will it fall on the earth or dumped in space?

Fall to earth. The only reason the space shuttle and other orbiting objects do not is that they are traveling so fast that they essentially fall around the earth, never approaching any closer. Your object is stationary relative to the surface, and the distance is such that gravity is more than 98 or 99 percent the same as at the surface. So, it falls

This Stick Will fall on Earth. First, the most important thing to know is that gravity exists absolutely everywhere in the universe. The force exerted depends on the distance of the object and the mass. Every bit of matter exerts a force on every other  matter. This means that you are attracted, and attract, everything in the universe!

consider a spinning top with a long stick on its head..Now this stick(and its tip) shows a very erratic motion when the top is spinning.Since any structure is not rigid shear and other forces would be acting on it.Hence the tower will break some where from the middle and fall on earth following a parabolic path.;