Final answer:
The Babcock clamp is the most commonly used instrument to grasp the mesoappendix during an appendectomy due to its design, which is suitable for holding delicate tissues such as the mesoappendix (option A).
Step-by-step explanation:
The instrument most commonly used to grasp the mesoappendix during an appendectomy is a Babcock clamp. The Babcock clamp is designed to hold delicate tissues without causing significant trauma. During appendectomy, it is essential to safely control the mesoappendix, which contains the blood vessels that supply the appendix. The Babcock clamp allows the surgeon to do this by gently grasping this tissue, which facilitates the ligation and cutting of the mesoappendix, thus separating it from the appendix itself.
Hence, the answer is option A.