D.1 Gravitational fields
Practice exam-style IB Physics questions for Gravitational fields, aligned with the syllabus and grouped by topic.
Question 1
A comet moves in an elliptical orbit around the Sun. What does Kepler's second law imply about the comet?
A.
It has zero acceleration at the farthest point from the Sun.
B.
It has its greatest speed when it is closest to the Sun.
C.
It takes equal times to move through equal distances along the orbit.
D.
It has constant speed throughout its orbit.
Question 2
Two point masses are separated by a distance and attract with force . The separation is changed to . What is the new force?
A.
$3F$
B.
$F/9$
C.
$9F$
D.
$F/3$
Question 3
The gravitational field strength at a point is best defined as the
A.
energy stored per unit volume of space at that point.
B.
work done per unit mass in moving a body to that point.
C.
force per unit mass on a small test mass at that point.
D.
force per unit area acting on a surface at that point.
Question 4
What do the arrows on gravitational field lines around an isolated planet show?
A.
The direction of the force on a small test mass.
B.
The direction in which the planet is moving.
C.
The direction of increasing gravitational force away from the planet.
D.
The path followed by every orbiting satellite.
Question 5
The gravitational potential energy of two separated masses is negative because
A.
the masses have negative gravitational field strength.
B.
the separation of two masses is always negative.
C.
the gravitational force is opposite to the velocity.
D.
energy must be supplied to separate the masses to infinity.
Question 6
Moving a mass along a gravitational equipotential surface at constant speed requires
A.
work equal to $mg\Delta r$.
B.
no work against gravity.
C.
work proportional to the path length only.
D.
work equal to its kinetic energy.
Question 7
State Kepler's first law.
[1]
State the meaning of the semi-major axis in Kepler's third law for an elliptical orbit.
[1]
Question 8
A small test mass of experiences a gravitational force of at a point.
Calculate the gravitational field strength at the point.
[1]
State why the test mass should be small.
[1]
Question 9
A planet may be treated as a point mass when calculating the gravitational force on a satellite if the satellite is
A.
outside a spherically symmetric planet.
B.
inside any hollow region of the planet.
C.
close enough that tides are large.
D.
larger than the planet's atmosphere.
Question 10
At a point on the line between two equal masses, exactly halfway between them, the resultant gravitational field strength is
A.
zero because the two field contributions are equal and opposite.
B.
towards the mass on the right.
C.
twice the field strength due to one mass.
D.
towards the mass on the left.
Question 11
A long spacecraft is near a small asteroid. The gravitational field at one end is measurably stronger than at the other end. What is the main reason the point-mass model for the spacecraft is poor?
A.
The spacecraft has no centre of mass.
B.
Newton's third law no longer applies.
C.
The asteroid must have no gravitational field.
D.
The field varies significantly across the spacecraft.
Question 12
The gravitational potential at radius from an isolated spherical planet is . What is the potential at radius ?
A.
$V_g/2$
B.
$2V_g$
C.
$V_g/4$
D.
$4V_g$
Question 13
A spacecraft of mass moves slowly from gravitational potential to . What is the work done by an external agent?
A.
$+4.0 imes10^7m\ ext{J}$
B.
$-8.0 imes10^7m\ ext{J}$
C.
$-4.0 imes10^7m\ ext{J}$
D.
$+8.0 imes10^7m\ ext{J}$
Question 14
At the same radius from a planet, the escape speed is related to the circular orbital speed by
A.
$v_{esc}=\sqrt{2}\,v_{orbital}$
B.
$v_{esc}=v_{orbital}$
C.
$v_{esc}=v_{orbital}/\sqrt{2}$
D.
$v_{esc}=2v_{orbital}$
Question 15
Two small asteroids of masses and are separated by .
Calculate the magnitude of the gravitational force between them.
[1]
State the direction of the force on each asteroid.
[1]
Question 16
A student calculates the force on a satellite by treating Earth as a point mass at its centre.
State one condition that allows this model to be used.
[1]
Explain why the same model may fail for calculating tidal effects on Earth due to the Moon.
[1]
Question 17
The diagram shows a single isolated spherical planet.
Sketch four gravitational field lines outside the planet.
[1]
State what is represented by closer spacing of field lines.
[1]
Question 18
Near Earth's surface, gravitational field strength is often taken to be uniform.
State one feature of a uniform gravitational field.
[1]
Explain why is equivalent to .
[1]
Question 19
Two spacecraft of masses and are separated by in deep space.
Calculate the gravitational potential energy of the two-spacecraft system.
[1]
State the physical meaning of the sign of your answer.
[1]
Question 20
A planet has mass . Determine the gravitational potential at a point from its centre. [3]
Question 21
A probe is moved without change in speed between two points where the gravitational potentials are and .
Calculate the work done by the external agent.
[1]
State whether the probe has moved to a higher or lower gravitational potential.
[1]
Question 22
The graph shows data for several moons orbiting the same planet.
State the relationship between and suggested by the graph.
[1]
Explain how the graph supports Kepler's third law.
[1]
Suggest one reason why a measured point may not lie exactly on the best-fit line.
[1]
Question 23
The graph shows the gravitational field strength at different distances from the centre of a spherical planet.
Describe how changes as increases outside the planet.
[1]
Use the graph to estimate the field strength at the planet's surface.
[1]
Explain why the graph is curved rather than a straight line outside the planet.
[1]
Question 24
The figure shows two students' sketches of gravitational field lines around the same spherical planet.
Identify which sketch better represents the field.
[1]
Give two reasons for your choice.
[1]
State one limitation of using field-line diagrams to represent gravitational fields.
[1]
Question 25
For circular orbits of small moons around the same planet, what is constant in the relationship ?
A.
$T$, because all moons orbit the same planet.
B.
$k$, because it depends on the mass of the planet.
C.
$r$, because the planet has a fixed radius.
D.
$T/r$, because orbital speed is the same for all moons.
Question 26
On a graph of gravitational potential against radial distance from a planet, the magnitude of gravitational field strength at a point is given by the
A.
area under the graph up to that point.
B.
intercept of the graph with the $V_g$ axis.
C.
magnitude of the gradient of the graph at that point.
D.
square of the potential at that point.
Question 27
A satellite is transferred from a lower circular orbit to a higher circular orbit. Which statement about the satellite in the final orbit is correct?
A.
Its kinetic energy is larger.
B.
Its gravitational potential energy is more negative.
C.
Its total mechanical energy is less negative.
D.
Its orbital speed is larger.
Question 28
A low-orbit satellite experiences a small atmospheric drag force for many orbits. What is the qualitative long-term effect?
A.
The orbital radius remains constant and only thermal energy changes.
B.
The orbital radius decreases and the orbital speed increases.
C.
The orbital radius increases and the orbital speed decreases.
D.
The orbital radius decreases and the orbital speed decreases.
Question 29
Two spherical bodies A and B lie on a straight line. A has mass and B has mass . Their centres are separated by distance .
At a point between A and B, state the directions of the gravitational field due to A and due to B.
[1]
Determine the distance from A, in terms of , at which the resultant gravitational field strength is zero.
[1]
Question 30
A planet moves around a star in an elliptical orbit.
State what happens to the planet's speed as it moves from its closest point to its farthest point from the star.
[1]
Explain your answer using Kepler's second law.
[1]
Question 31
The gravitational potential changes from to over an outward radial displacement of .
Determine the average gravitational field strength over this interval.
[1]
State the direction of the field.
[1]
Question 32
The diagram shows two gravitational equipotential surfaces near a planet.
Draw the direction of the gravitational field line crossing the surfaces.
[1]
Explain why gravitational field lines must be perpendicular to equipotential surfaces.
[1]
Question 33
A small object is at distance from the centre of a planet of mass .
Calculate the escape speed from this point.
[1]
State whether this escape speed depends on the mass of the object.
[1]
Question 34
A satellite is in a circular orbit of radius around a planet of mass .
Calculate the orbital speed.
[1]
Calculate the orbital period.
[1]
Question 35
A low-Earth satellite experiences a small drag force from the upper atmosphere.
State what happens to the total mechanical energy of the satellite–Earth system.
[1]
Explain why the speed of the satellite can increase as its orbit decays.
[1]
Question 36
A student investigates the gravitational force between a fixed mass and a small test mass at different separations. The graph shows against .
State why plotting against is useful.
[1]
Use the gradient of the graph to determine the product .
[1]
Explain why the graph should pass through the origin.
[1]
Suggest one practical difficulty in measuring gravitational forces between laboratory masses.
[1]
Question 37
The diagram shows the gravitational field strength along the line joining two spherical bodies X and Y.
Identify a position where the resultant gravitational field strength is zero.
[1]
Explain why the zero-field point is closer to the smaller mass.
[1]
State the direction of the resultant field at a point between the zero-field point and the larger mass.
[1]
Suggest how the position of the zero-field point would change if the mass of Y were increased.
[1]
Question 38
The graph shows gravitational potential as a function of radial distance from the centre of a planet.
State the value approached by as becomes very large.
[1]
Use the graph to determine the change in potential between two marked radii.
[1]
Calculate the work done by an external agent in moving a probe of given mass between the marked radii without changing its speed.
[1]
Explain why the potential values are negative.
[1]
Question 39
A potential map for a region near a small spherical moon is shown using equipotential lines.
Draw an arrow showing the direction of the gravitational field at point P.
[1]
Identify where the gravitational field is greatest on the map.
[1]
Estimate the magnitude of the field strength at P using adjacent equipotential lines.
[1]
Explain why no work is done by gravity when a mass moves along one equipotential line at constant speed.
[1]
Question 40
The table gives data for a satellite in two circular orbits around the same planet.
| Quantity | Symbol | Value / SI unit |
|---|---|---|
| Mass of planet | M | 5.97 × 10^24 kg |
| Mass of satellite | m | 1.20 × 10^3 kg |
| Lower orbital radius | r₁ | 7.00 × 10^6 m |
| Higher orbital radius | r₂ | 4.20 × 10^7 m |
Calculate the orbital speed in the lower orbit.
[1]
Calculate the total mechanical energy in each orbit.
[1]
Determine the minimum energy that must be supplied to transfer the satellite from the lower circular orbit to the higher circular orbit, ignoring losses.
[1]
Explain why the satellite has a smaller speed in the higher orbit although energy has been supplied.
[1]
Question 41
The graph shows the radius and speed of a low-orbit satellite over many orbits as it experiences atmospheric drag.
Describe the trend in orbital radius.
[1]
Describe the trend in orbital speed.
[1]
Explain why these two trends can occur at the same time.
[1]
Question 42
A newly discovered asteroid is observed to orbit the Sun in a noticeably elliptical orbit.
State Kepler's three laws as they apply to this asteroid.
[1]
Discuss how a circular-orbit model can still be useful, and give two limitations of using it for this asteroid.
[1]
Question 43
A mission designer models a moon, a spacecraft and a nearby asteroid as point masses.
State two situations in which an extended body may be treated as a point mass in gravitational calculations.
[1]
Evaluate the usefulness and limitations of the point-mass model for this mission, including reference to tidal effects and centre of mass.
[1]
Question 44
Gravitational fields near Earth's surface are often drawn as uniform, while fields around planets are drawn as radial.
Describe how field lines represent magnitude and direction of gravitational field strength.
[1]
Compare and contrast a uniform gravitational field near a surface with the radial gravitational field around an isolated spherical planet.
[1]
Question 45
The graph shows kinetic energy, gravitational potential energy and total mechanical energy for a probe launched vertically from the surface of a small airless planet.
Identify the graph that represents total mechanical energy for a launch at exactly escape speed.
[1]
Explain the energy condition for escape.
[1]
Use the surface data on the graph to estimate the escape speed of the probe.
[1]
Suggest why the actual launch speed from a planet with an atmosphere would need to be greater.
[1]
Question 46
Two planets lie on a straight line. Planet A has mass and planet B has mass . Their centres are separated by .
Derive an expression for the gravitational field strength due to a spherical planet outside its surface.
[1]
Determine the position between the planets where the resultant gravitational field strength is zero, and explain why there is no zero-field point outside the two planets on this line.
[1]
Question 47
A satellite of mass moves from an initial circular orbit of radius to a higher circular orbit of radius around a planet of mass .
Derive the expression for the total mechanical energy of a satellite in a circular orbit.
[1]
Explain, using energy ideas, why work must be done to move the satellite to the higher circular orbit even though its final orbital speed is smaller.
[1]
Question 48
Gravitational potential is used to describe fields around planets.
Define gravitational potential and state its expression for a point mass.
[1]
Discuss how gravitational potential, gravitational potential energy and gravitational field strength are related, including the significance of signs.
[1]
Question 49
A satellite in low orbit experiences a small viscous drag force from the upper atmosphere.
State the changes in total mechanical energy, gravitational potential energy and kinetic energy as the orbit decays gradually.
[1]
Evaluate the statement: "Atmospheric drag always makes an orbiting satellite slower."
[1]
Question 50
A spacecraft is initially at rest on the surface of a non-rotating airless planet of mass and radius . It is to be placed into a circular orbit of radius .
Show that the ideal energy needed per unit mass is .
[1]
Evaluate the additional energy condition for the spacecraft to escape from that circular orbit, and compare the required escape speed with the orbital speed.
[1]
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