The directive force of a gyrocompass __________.

Correct Answer: Option C — decreases with latitude, being maximum at the geographic equator

The directive force of a gyrocompass is proportional to the horizontal component of the Earth's rotation. This component is maximum at the equator and decreases as latitude increases, reaching zero at the poles. Consequently, the gyrocompass loses its ability to seek the meridian as it approaches the geographic poles.