Gravitation - gravity force, centripetal aceleration, work

[joanneadams]

1Problem:
Two equal satellite, A and B, of a planet of mass M, describe circular trajectories where the radious are 0,5r and r. We can afirm that:
A- The intensity of gravitical force acting on B is half of the gravitical force acting on A;
B- The value of centripetal aceleration of A is one quarter of the value of centripetal aceleration of B.
C- The gravitic potencial energy of the sistem planet+B is double of the gravitic potential energy of the sistem planet+A.
D The work done by the gravitical force, during a complete turn, to satellite A is doubble of the work done by satelite B.

Useful equations:
Fg=G x (mM)/r²

a_c=GM/r²

Epg=-GmM/r

Atempt of solution:
I think the right answer is option D.
A- is wrong because it's not half, is one quarter
B.- It's wrong because it's not one quarte, its four times
C- I think it's wrong because it's one half, and not double
D- Both of them are zero, and tecnically 0 times 2 is zero
But my teacher says it's option C, because she says is a negative number. I don't agree with her because, if we do the math we get Epg(B)=1/2Epg(A). why am i wrong, how can C be the right option?
Thank you, for your atention and sorry for the bad english...

 

[stockzahn]

Two equal satellite, A and B, of a planet of mass M, describe circular trajectories where the radious are 0,5r and r.

C- The gravitic potencial energy of the sistem planet+B is double of the gravitic potential energy of the sistem planet+A.

C- I think it's wrong because it's one half, and not double

Two equal masses ($m_A =m_B$), let's say rocks, are located at different heights ($h_A, h_B$) from the ground, where $2\cdot h_A =h_B$. Which of them would you expect to have a higher potential energy?

 

[gneill]

Hi joanneadams,

Welcome to Physics Forums!

But my teacher says it's option C, because she says is a negative number.

Like you I don't see what the sign has to do with it! I agree with you on that point.

Regarding choice D, with the works both being zero it is meaningless to claim that one is twice the other. If you did allow that you could prove that any number is equal to any other number; you'd "break" mathematics

 

[Orodruin]

At face value, C is ill defined unless you also specify the reference level. With the reference level at infinity, B (assuming it is the satellite further away) will have a larger potential than A and indeed, since the numbers are negative, you will obtain $V_A = 2V_B$.

When it comes to D, I agree with you. Since the work is zero in both cases, the work done on A will indeed be twice the work done on B since $2\cdot 0 = 0$.

 

[Orodruin]

Regarding choice D, with the works both being zero it is meaningless to claim that one is twice the other. If you did allow that you could prove that any number is equal to any other number; you'd "break" mathematics

I disagree. Zero is exactly the same as two times zero. The statement as given is clearly true. If you take the work done on B and multiply it by two, you get a number that is the work done on A. In other words, $x = y = 0$ is a valid solution to the equation $y = 2x$, which the given statement translates to.

 

[gneill]

I disagree. Zero is exactly the same as two times zero. The statement as given is clearly true. If you take the work done on B and multiply it by two, you get a number that is the work done on A. In other words, $x = y = 0$ is a valid solution to the equation $y = 2x$, which the given statement translates to.

Fine. I stand corrected.

I think that, on the whole, the question is poorly designed and presented.

 

[Orodruin]

I think that, on the whole, the question is poorly designed and presented.

On this, I definitely agree.