To solve this problem, we need to understand why a gymnast can balance his body upside down even in total darkness. This ability is related to the body's sense of balance and spatial orientation.$\newline$Let's analyze each option:$\newline \bullet$Cochlea:$\newline$ - The cochlea is a part of the inner ear involved in hearing. It converts sound waves into nerve impulses.$\newline$ - It is not directly involved in balance.$\newline \bullet$Vestibular apparatus:$\newline$ - The vestibular apparatus is a part of the inner ear that is crucial for maintaining balance and spatial orientation.$\newline$ - It includes structures such as the semicircular canals, which detect rotational movements, and the otolith organs, which detect linear accelerations.$\newline$ - This system helps the body maintain balance even in the absence of visual cues, such as in darkness.$\newline \bullet$Tectorial membrane:$\newline$ - The tectorial membrane is part of the cochlea and plays a role in the auditory system.$\newline$ - It is not involved in balance.$\newline \bullet$Organ of Corti:$\newline$ - The organ of Corti is located within the cochlea and is responsible for detecting sound vibrations.$\newline$ - It does not contribute to balance.$\newline$Based on this analysis, the vestibular apparatus is responsible for the gymnast's ability to balance his body upside down in total darkness.$\newline$Therefore, the correct option is Option 2: Vestibular apparatus.