I haven't been able to get the fragments of the green object to explode. I'm not sure why, since I added physics, rigid bodies and made it active.
Here's a screenshot:
Here is the .blend:
Your object that you want to explode is one solid object. In order for it to explode you must first break it up into pieces.
I took the following steps:
Object mode run cell fracture
Move object on layer one to a secondary/ unused layer and move fractures to layer one