- #1

AN630078

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- 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?

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?