Which of the following describes a belt-fed, recoil operated air cooled machine gun?

The description of a belt-fed, recoil operated air-cooled machine gun is most accurately represented by the .50 caliber machine gun. This type of machine gun, such as the M2 Browning, is known for its high rate of fire and significant stopping power, features that are characteristic of .50 caliber systems.

Belt-fed operation means that ammunition is supplied to the gun continuously via a belt, allowing for sustained fire without frequent reloading. The recoil operation system utilizes the backward motion generated when a round is fired to help cycle the action, making it efficient for automatic fire.

While the .30 caliber and 7.62 mm machine guns are also belt-fed and recoil-operated, they are generally lightweight and designed for different roles compared to the powerful .50 caliber which is often used in heavy machine gun applications, capable of penetrating armor and used against both ground and aerial targets. The 9 mm is primarily a pistol caliber and does not fit the description of a machine gun at all. Therefore, the .50 caliber machine gun is the correct choice in this context.