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The correct answer here is B -- the weight of the rocket decreases.
The point of this question appears to be the difference between weight and mass. Mass is a measure of the amount that is in an object. By definition, then, the mass of the rocket would not change as it moved away from Earth (not including, of course, the fuel it is burning).
However, weight is a measure of how strongly gravity pulls on a given object. As the rocket moves away from Earth, the pull of the Earth's gravity on the rocket weakens. So the weight of the rocket decreases.
Of course, if the rocket goes far enough and in the right direction, it might get heavier again as it comes under the influence of the gravitational attraction of some other body.
The force between the rocket and the earth if the gravitational attraction which is proportional to the gravitational constant, G times Mass of earth,M and mass of the rocket, m divided by the square of the distance between them (that is ,the distance between their centre of masses) . On the surface of earth, R = radius of earth and this force is equal to GMm/R^2 = 6.673*5.8*10^24/(6137000)^2 = 9.83m/s^2 or g, the acceleration due to gravity and it is also mg, the weight on the surface of earth. But as the the rocket goes up, the R increases and the gravitational attraction between the rocket and the earth, which nothing but the weight of the rocket at the distance R from earth, goes inversely proportional to the square of the distance . That is, the weight of the rocket is inversely proportional R^2. Thus the weight reduces as the rocket goes away from the earth.
B. The weight of the rocket decreases.
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