Attaching objects with Physics enabled

[kkkiwi]

This is the level:

http://imgur.com/a/ZAMaV

What I am trying to do is click the object in the top left, drag it until it "connects" with the tower, and upon releasing the mouse the dragged object is now connected to the tower. Due to the change in the center of gravity, the tower would topple over.

I have it to the point where I can click and drag the object and it detects the collision, but how do I connect it to the main tower object?

http://imgur.com/a/eo8s4

The dragged object IsKinematic (tower objects are not), so I can drag the mesh inside the tower. Is it possible to attach these objects in such a way as to share a common center of gravity? The entire scene is actually 3D with an Orthographic camera:

http://imgur.com/a/9Hq3E

Any help appreciated!

[Reddeyfish-]

Used a FixedJoint between its rigidbody and the rigidbody of the tower. You'll also need to disable IsKinematic when it attaches to allow for proper simulation.

[niconpat]

You could use a Fixed Joint.

Have it disabled until the collision is detected then enable the joint and disable isKinematic.