A space rocket travels to the Moon. The acceleration of free fall is greater on the Earth than it is on the Moon. How do the mass and weight of the space rocket on the Moon compare with their values on Earth?

 In this problem, it is important to establish in mind that mass and weight are two different things. Mass is a fundamental dimension which refers to the quantity of the matter while weight is a fundamental dimension that refers to the product of mass and the acceleration due to gravity.

Mass is a fundamental property of matter and is a measure of the amount of material in an object. It is a scalar quantity and is typically measured in kilograms (kg) in the International System of Units (SI). Mass is an intrinsic property of an object and remains the same regardless of its location. In simpler terms, if you were to take a space rocket from Earth to the Moon, its mass would remain constant. This is because mass is a measure of the amount of matter an object contains, and this amount doesn't change as you move the object from one location to another.

On the other hand, weight is a measure of the force exerted on an object due to gravity. It is a vector quantity, meaning it has both magnitude and direction. Weight is dependent on the gravitational field strength of the celestial body the object is on. On Earth, the gravitational acceleration is approximately 9.8 meters per second squared ( ). This means that every kilogram of mass experiences a force of about 9.8 Newtons (N) due to gravity.

However, the gravitational field strength on the Moon is significantly weaker than on Earth. The Moon's gravitational acceleration is about one-sixth (1/6) that of Earth's, approximately . Therefore, the weight of an object on the Moon is only about one-sixth of its weight on Earth.

Thus, the answer must be C, The mass on the Moon is the same as on the Earth and the weight on the Moon is less than the weight on the Earth.