# Gravitational Field Multiple Choice Help

• AN630078
That is, shells whose potential difference from the mass is the same. For a spherically symmetric field, the potential difference from the mass is the same on the shell as at the mass. So the potential difference between shells of radius r and r+Δr is the same as that between shells of radius R and R+ΔR. That means they are equally spaced in the sense of equal potential difference between successive shells. But the shells are not equally spaced in the sense of equal distance between them, which is what we mean by equally spaced in general.

#### AN630078

Homework Statement
Hello, I have been revising material concerning gravitational fields and have been using various multiple choice questions I have found online to test my knowledge. I think I actually struggle with MC questions as they often appear quite simplistic initially but then require further calculation or applied knowledge. Furthermore, the questions I found did not accompany a mark scheme and I am rather curious to see whether my reasoning would be correct so I have selected a few of the questions and attached them below. If anyone could offer their thoughts or any further guidance to approaching such problems I would be very grateful

1. A satellite is orbiting a large planet at a distance r from its centre. If r increases what would happen to the gravitational potential and the gravitational field?

2. Which of the following is not a possible unit for gravitational field strength?
i.Nkg^-1
ii. Jm^-1kg^-1
iii. Nm^2kg^-1
iv. ms^-2

3. When a satellite doubles its distance from the centre of a planet...
i.The magnitude of the gravitational potential is halved, and the gravitational force becomes a quarter of its former magnitude.
ii.The magnitudes of the gravitational force and the gravitational potential are halved.
iii.The gravitational force becomes a quarter of its former magnitude but the gravitational potential remains the same.
iv.Both the gravitational force and the gravitational potential are reduced to a quarter of their
former magnitude.

4. A uniform gravitational field is drawn to show the gravitational field lines and the equipotential surfaces (for equal increments of energy) .
i.Neither the equipotential surfaces nor the field lines are equally spaced.
ii.The field lines are equally spaced, but the equipotential surfaces are unequally spaced.
iii.The equipotential surfaces are equally spaced, but the field lines are not.
iv. Both field lines and equipotential surfaces are equally spaced and parallel.

5. A radial gravitational field is drawn to show the gravitational field lines and the equipotential surfaces (for equal increments of energy)
i.Neither the equipotential surfaces nor the field lines are equally spaced.
ii.The field lines are equally spaced, but the equipotential surfaces are unequally spaced.
iii.The equipotential surfaces are equally spaced, but the field lines are not.
iv. Both field lines and equipotential surfaces are equally spaced and parallel.
Relevant Equations
g∝1/r^2
1. I believe that the gravitational field strength would decrease because it is inversely proportional to the square of the distance from the centre of the Earth, g∝1/r^2.
Gravitational potential energy at large distances is directly proportional to the masses and inversely proportional to the distance between them. The gravitational potential energy would therefore decrease as r increases.

2. I am very uncertain here. I understand that the units for gravitational field strength are Nkg^-1, which is equivalent to the unit of metre per second squared, ms^-2. So the answer is not i or iv. And since 1 Joule = 1 Newton * m, would Jm^-1kg^-1 be equivalent to Nkg^-1?
However, I know that the unit for gravitational constant G is m3⋅kg^−1⋅s^−2 which is equivalent to iii. Nm2kg^-1, so would this be the unit that is not possible for g?

3. I believe that the gravitational force would decrease because it is inversely proportional to the square of the distance from the centre of the Earth, F∝1/r^2. So as r doubles it would become a quarter of its previous value.
Gravitational potential energy at large distances is directly proportional to the masses and inversely proportional to the distance between them. So I think the gravitational potential would halve. (option i)

4. Would the correct answer be iv, since the gravitational field lines in a uniform field would be perfectly parallel and the evenly spaced equipotentials in a uniform field such as that close to the Earth are perpendicular to such field lines.

5. The gravitational field is not uniform (the field lines are never parallel or equi-spaced) so as you move away from the object, the strength of the field reduces. Gravitational field lines are perpendicular to equipotential surfaces, which are spherical and show an increase in the spacing between them as distance from the centre of the mass increases. Therefore, would neither the equipotential surfaces nor the field lines be equally spaced in a radial field?

1: Field Strength decreases - I agree.
Look up the definition of Gravitational Potential and try again. Gravitational Potential is relative to a point of reference. That point of reference is normally taken to be infinity - thus making the potential negative at all points.

2: The question is giving you a big clue here. Three of those can be converted from one to another. One is different.

3: I agree.

4: I agree.

5: It's a little odd to call intersecting lines "equally spaced", but I would answer "ii". For any given potential, they are equally spaced.

AN630078
AN630078 said:
Gravitational potential energy at large distances is directly proportional to the masses and inversely proportional to the distance between them. The gravitational potential energy would therefore decrease as r increases.
In case @.Scott 's reply is unclear, the proportionality is to ##-\frac 1r##. As ##\frac 1r## decreases, ##-\frac 1r## increases.
AN630078 said:
The gravitational field is not uniform ... so as you move away from the object, the strength of the field reduces.
But the equipotentials could still be equally spaced.
How can you show they are not?
AN630078 said:
Gravitational field lines are perpendicular to equipotential surfaces, which are spherical and show an increase in the spacing between them as distance from the centre of the mass increases
For the field lines, the question probably means equally spaced in the sense of equal angles between them. It should have been made clearer.

AN630078
1. So the gravitational field strength decreases but the gravitational potential increases?
5. If the gravitational field line have equal angles between them then they are equally spaced, but the equipotential surfaces are unequally spaced.
The gravaitational potential for a mass is the same anywhere on a sphere of radius r, and thus has the same value at any point that is a given distance from the mass. Is this why the equipotential surfaces are unevenly spaces, as they must represent the same potential?

.Scott said:
1: Field Strength decreases - I agree.
Look up the definition of Gravitational Potential and try again. Gravitational Potential is relative to a point of reference. That point of reference is normally taken to be infinity - thus making the potential negative at all points.

2: The question is giving you a big clue here. Three of those can be converted from one to another. One is different.

3: I agree.

4: I agree.

5: It's a little odd to call intersecting lines "equally spaced", but I would answer "ii". For any given potential, they are equally spaced.

AN630078 said:
1. So the gravitational field strength decreases but the gravitational potential increases?
Yes. With the standard convention that the potential is zero at infinity, the increase is in the sense that it becomes less negative.
AN630078 said:
5. If the gravitational field line have equal angles between them then they are equally spaced
Equally spaced in the sense of angular spacing, yes.
AN630078 said:
The gravaitational potential for a mass is the same anywhere on a sphere of radius r, and thus has the same value at any point that is a given distance from the mass. Is this why the equipotential surfaces are unevenly spaces,
No.
First, what would we mean by saying the equipotentials are equally spaced? With a spherically symmetric field, all concentric spherical shells are equipotentials. It is a continuum, so there is no 'spacing' as such. The only reasonable interpretation is that if you draw equipotentials at equal intervals of potential difference then they won't be equally spaced.
So to answer the question you must consider successive shells at equal intervals of potential difference.