12. An astronaut travels to the Moon, where the magnitude of the force of gravity is one-sixth the magnitude of the force of gravity on Earth. On the Moon, which of the following is true?
Answer: B
The astronaut's weight is one-sixth of his weight on Earth.
On the Moon, the astronaut experiences a force of gravity that is one-sixth that of Earth, which directly affects his weight. Since weight is the product of mass and gravitational acceleration, the astronaut's weight on the Moon would indeed be one-sixth of what it is on Earth.
A) The astronaut's mass is one-sixth of his mass on Earth.
This statement is incorrect because mass is a measure of the amount of matter in an object and does not change regardless of the gravitational field. The astronaut's mass remains the same whether he is on Earth or the Moon.
B) The astronaut's weight is one-sixth of his weight on Earth.
This statement is correct. Weight is dependent on both mass and the local gravitational acceleration. Since the Moon's gravity is one-sixth that of Earth's, the astronaut's weight on the Moon is consequently one-sixth of his weight on Earth.
C) The astronaut's mass is six × his mass on Earth.
This statement is incorrect because it suggests that the astronaut's mass increases when he is on the Moon. Mass remains constant regardless of location, so it cannot be six times greater on the Moon.
D) The astronaut's weight is six × his weight on Earth.
This statement is incorrect as it contradicts the relationship between weight and gravitational force. Given that the Moon's gravity is one-sixth that of Earth, the astronaut's weight cannot be six times greater; it is actually one-sixth.
Conclusion
The correct answer is B, as it accurately reflects the relationship between weight and gravitational force. All other options fail because they either misinterpret the concept of mass or incorrectly apply gravitational principles, highlighting the importance of distinguishing between mass and weight in different gravitational contexts.