Gravitational equipotential multiple choice problem

[Grizzly_1]

Homework Statement

The diagram shows gravitational equipotential. Adjacent equipotential are separated by an equal gravitational potential difference V.

Which point has the greatest gravitational field strength?

Relevant Equations

E=-GM/(r^2)

Hello everyone, thank you for taking your time to read this. I was assigned a homework task of multiple choice questions to do with gravitational fields. This is one of the last questions and I have been pondering over it for some time now. I don't understand how any sort of answer is achievable.

To the best of my knowledge, gravitational field strength is directly proportional to the mass of the object that is causing the field, and inversely proportional to the square of the distance between the mass causing the field and the point at which you are determining field strength. In this case, as we do not know the location of the mass we cannot determine the direction of the field lines, and by extension we cannot tell if the potential differences are decreasing from D to A, or A to D.

If you knew which way the potential gradient was increasing, I think you could work out which point had the greatest gravitational field strength as it is the point at which potential is the least (most negative), as this implies it is closest to the mass or masses that are causing the field.

As you do not know this, I do not know how you could answer such a question, they are just arbitrarily placed about the square and I do not know the relevance of equipotentials, as these are just indications about lines that have an equal potential difference along its length, this doesn't tell us anything relevant to finding at which point the gravitational field is greatest.

So this is my reasoning so far, I am truly stumped. I hope someone can help out in solving this tricky question (or perhaps not tricky and I am just being silly).

​

 

[berkeman]

On a topographical map of terrain on the Earth, how can you tell the steepest parts from those that are flatter?

 

[kuruman]

Does this help?

 

[Grizzly_1]

Does this help?
View attachment 325485

On a topographical map of terrain on the Earth, how can you tell the steepest parts from those that are flatter?

Hello, thank you for responding. I understand both of your comments (I think), you are saying that, in the area were the equipotential lines are closest together, there must be a greater potential difference gradient, and therefore a greater field strength. I now understand, you have both helped me greatly. Thank you again!

 

[kuruman]

Hello, thank you for responding. I understand both of your comments (I think), you are saying that, in the area were the equipotential lines are closest together, there must be a greater potential difference gradient, and therefore a greater field strength. I now understand, you have both helped me greatly. Thank you again!

You got it!