The component of the ear that is primarily responsible for balance is:

The semicircular canals are the components of the inner ear that play a crucial role in maintaining balance and equilibrium. They are three fluid-filled structures positioned at right angles to one another, allowing the detection of rotational movements of the head. When the head moves, the fluid within these canals shifts, which in turn activates hair cells lining the canals. These hair cells send signals to the brain regarding the position and movement of the head, helping to maintain balance and coordination.

In contrast, the cochlea is primarily responsible for hearing, converting sound waves into neural signals. The Eustachian tube's function is to equalize pressure in the middle ear and does not have a role in balance. The auditory nerve transmits auditory information from the cochlea to the brain, again focusing on sound rather than balance-related functions. Thus, the semicircular canals are specifically designed for balance, making them the correct choice for this question.