ExamKrackers: Gravitational Force Question

[Lunasly]

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Two plants have the same mass but different radii. Each has a moon with the same orbital radius. Compared to the smaller planet, the larger planet attracts its moon with a gravitational force that is:

A) Greater
B) Smaller
C) The same
D) The gravitational force depends upon the masses of the moons.

Answer: D (highlight)

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I understand that the masses of the moons is going to play a role here since an increase or decrease in mass for either is directly proportional to the gravitational force. However, doesn't radii also have an effect (indirectly proportional)? Since the radii is squared while the mass isn't, wouldn't it play a larger role?

 

[osprey099]

Two plants have the same mass but different radii. Each has a moon with the same orbital radius. Compared to the smaller planet, the larger planet attracts its moon with a gravitational force that is:

A) Greater
B) Smaller
C) The same
D) The gravitational force depends upon the masses of the moons.

Answer: D (highlight)

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I understand that the masses of the moons is going to play a role here since an increase or decrease in mass for either is directly proportional to the gravitational force. However, doesn't radii also have an effect (indirectly proportional)? Since the radii is squared while the mass isn't, wouldn't it play a larger role?

Well, the question doesn't say the masses of the two moons so I am going to assume that the moons have the same masses. This will make B the correct answer because F(gravitational) = GMm/R^2 where R is the distance between the center of one object to the center of the other object. If you have a larger planet, this means that it has a bigger radius so F(gravitational) for the larger planet and its moon is smaller.

 

[Lunasly]

That is the same train of thought that I had, but the answer is D. Because they didn't give us the masses of the moons, then we can't assume that they are of equal mass and so choice D is the correct answer :\

 

[osprey099]

That is the same train of thought that I had, but the answer is D. Because they didn't give us the masses of the moons, then we can't assume that they are of equal mass and so choice D is the correct answer :\

Oh yea your right. I completely didn't look at choice D lol. But yea, mass does have an effect because F = GMm/r^2. The mass that choice D refers to is the small "m." You need to know the mass because even though radius is squared, the difference in radius between the two planets can be very small and the difference in mass between the two moons can be very large so in that case, the mass effect is bigger than the radius effect.