Physics for dynamically digging through 2D terrain

Is there a way in Unity to have 2D terrain modifiable in game in a very fluid way? See the attached image for a better idea of what I mean. User drags the cursor or finger over the terrain to 'dig it'. Ball's physics adjust accordingly and falls down. Just wondering if anyone would be able to let me know if this is possible or how to get started on something like this? Thanks.