Final answer:
Mediastinoscopy is the study that should be used to investigate a 2cm lymph node off of the right mainstem bronchus.
Step-by-step explanation:
To investigate a 2cm lymph node off of the right mainstem bronchus, a medical professional would typically use a procedure called mediastinoscopy. This procedure involves making a small incision in the neck and inserting a thin tube with a camera attached to it into the chest to examine the lymph node. Biopsy samples may also be taken during the procedure for further analysis.