Which component of a lensatic compass is mounted on a pivot and rotates freely?

The correct answer is the floating dial. The floating dial is a crucial component of a lensatic compass as it contains the markings indicating directions and it rotates freely on a pivot. This design allows the floating dial to align with the magnetic field, enabling the user to determine true north based on the position of the magnetic needle. The ability to pivot is essential for accurately reading the direction, as the dial will respond to the Earth's magnetic field and align itself accordingly.

The base plate serves as the foundation of the compass and holds other components in place. It does not rotate. The magnetic needle, while being an essential component for indicating north, is not mounted on a pivot; it is typically fixed in a way that allows it to point freely due to magnetic attraction. The index line is a stationary feature on the base plate that indicates the direction the user is facing but does not have any rotation capability. Therefore, the floating dial’s ability to rotate freely on a pivot is what makes it the correct answer.