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The hot air in the balloon is less dense than the cooler air in the atmosphere.

The buoyancy of the hot-air balloon is primarily due to the fact that the hot air inside the balloon is less dense than the cooler air surrounding it. This difference in density allows the balloon to rise as the denser, cooler air pushes it upward.

A) has a lower pressure than the atmospheric pressure

While pressure differences play a role in buoyancy, the key factor in the balloon's ability to rise is density, not pressure alone. The hot air inside the balloon may have a lower pressure, but it is the lower density relative to the cooler air that enables it to ascend.

B) is less dense than the cooler air in the atmosphere

This option accurately describes the principle of buoyancy that allows the hot-air balloon to rise. The hot air expands and becomes less dense than the surrounding cooler air, resulting in an upward force that lifts the balloon.

C) has more inertia than the cooler air in the atmosphere

Inertia is not a significant factor in the rising of a hot-air balloon. In fact, the principle of buoyancy is determined by density differences rather than inertia, making this option incorrect.

D) contains one gas only, whereas the atmosphere is a mixture of gases

The composition of gases inside the balloon versus the atmosphere does not directly relate to the balloon's ability to rise. The buoyant force is dependent on density differences rather than the number of gas types, making this option incorrect.

Conclusion

The correct answer, that the hot air in the balloon is less dense than the cooler air in the atmosphere, directly explains the buoyancy effect that allows the balloon to rise. All other options fail to address the primary principle of density, which is essential for understanding the mechanics of hot-air balloon flight.