The mass will go into orbit.
Have a look at this extract from wikipedia:
"Space tower
A space tower is a tower that would reach outer space. To avoid an immediate need for a vehicle launched at orbital velocity to raise its perigee, a tower would have to extend above the edge of space (above the 100 km Kármán line), but far lesser tower height could reduce atmospheric drag losses during ascent. Satellites can orbit temporarily in elliptical orbits dipping as low as 135 km or less, yet orbital decay causing reentry would be rapid unless altitude was later raised to hundreds of kilometers.[20] If the tower went all the way to geosynchronous orbit at approximately 36,000 km, or 22,369 miles, objects released at such height could then drift away with minimal power and would be in a circular orbit. Building a tower to that extreme height is not possible with current materials on Earth. The concept of a structure reaching to geosynchronous orbit was first conceived by Konstantin Tsiolkovsky,[21] who proposed a compression structure, or "Tsiolkovsky tower"."
Have a look at this extract from wikipedia:
"Space tower
A space tower is a tower that would reach outer space. To avoid an immediate need for a vehicle launched at orbital velocity to raise its perigee, a tower would have to extend above the edge of space (above the 100 km Kármán line), but far lesser tower height could reduce atmospheric drag losses during ascent. Satellites can orbit temporarily in elliptical orbits dipping as low as 135 km or less, yet orbital decay causing reentry would be rapid unless altitude was later raised to hundreds of kilometers.[20] If the tower went all the way to geosynchronous orbit at approximately 36,000 km, or 22,369 miles, objects released at such height could then drift away with minimal power and would be in a circular orbit. Building a tower to that extreme height is not possible with current materials on Earth. The concept of a structure reaching to geosynchronous orbit was first conceived by Konstantin Tsiolkovsky,[21] who proposed a compression structure, or "Tsiolkovsky tower"."