IBPhysicsHLTopic QuestionsFieldsGravitational Fields

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Gravitational Fields (HL IB Physics)

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Gravitational Fields

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Gravitational Fields

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1
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What is the correct relationship between the gravitational force and the distance between two point masses?

  • F proportional to 1 over G

  • F proportional to 1 over m

  • F proportional to 1 over r squared

  • F proportional to r squared

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2
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The force, F between two point masses is 10 N. The distance, r between the two masses is doubled. 

What is the new force between the two masses?

  • 2.5 N

  • 5 N

  • 20 N

  • 100 N

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3
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The gravitational force, FG as shown on the diagram, keeps the Earth orbiting the Sun in a circular orbit.

6-2-newtons-law-of-gravitation-sl-mcqs-easy-q3-question

What type of force is FG?

  • Electrostatic force

  • Centripetal force

  • Centrifugal force

  • Contact force

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4
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Which expression best describes the relationship between the orbital time period, T and the orbital radius, r?

  • T cubed proportional to r squared

  • T squared equals r cubed

  • T squared proportional to 1 over r cubed

  • T squared proportional to r cubed

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5
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Which of the following is not an equation which can be used to calculate g, the gravitational field strength?

  • g equals F over m

  • g equals fraction numerator G M over denominator r squared end fraction

  • g equals F m

  • g equals fraction numerator w e i g h t over denominator m a s s end fraction

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6
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Which of the following statements about gravitational force is true?

  • Gravitational force has a finite range

  • A greater gravitational force is exerted on objects with larger mass

  • On planets with a large value of g, the gravitational force per unit mass is smaller than on planets with a smaller value of g

  • An object's mass changes depending on the gravitational field strength at that point

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7
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An alien of mass 100 kg lives on a planet with a gravitational field strength of 50 N kg−1. 

What is the weight of the alien on this planet?

  • 5000 N

  • 1000 N

  • 0.05 N

  • 100 N

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8
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A planet has twice the radius of the Earth and 4 times the mass. Assume the planet is spherical and of uniform density.

If the magnitude of the gravitational field strength on Earth is g, what is the magnitude of the gravitational field strength on the surface of the planet?

  • 4g

  • 8g

  • 2g

  • g

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9
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Which graph, plotted on logarithmic axes, shows Kepler's Third Law for the planets in our Solar System?

  • 6-2-newtons-law-of-gravitation-sl-mcqs-easy-q10-answer-a

  • 6-2-newtons-law-of-gravitation-sl-mcqs-easy-q10-answer-b

  • 6-2-newtons-law-of-gravitation-sl-mcqs-easy-q10-answer-c

  • 6-2-newtons-law-of-gravitation-sl-mcqs-easy-q10-answer-d

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10
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The gravitational field strength at a point P in a gravitational field is defined as:

The force...

  • per unit mass on a mass placed at P

  • on a mass placed at P

  • per unit mass on a small point mass placed at P

  • on a small point mass placed at P

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11
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Which of the following correctly describes the value of the gravitational potential at a point infinitely far away from every massive body in the universe? 

  • infinity

  • negative infinity

  • 0

  • pi

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12
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Which of the following statements regarding gravitational potential is incorrect?

  • It is analogous to the electric potential at a point in an electric field

  • It is a vector quantity

  • It is defined as negative because work must be done on a mass to move it to infinity

  • It is inversely proportional to the distance between masses

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13
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What are the standard units of gravitational potential?

  • J

  • V

  • N kg–1

  • J kg–1

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14
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When a mass is moved against the force of gravity, work is done such that the change in work done, ΔW is equal to the change in gravitational potential ΔV.

Which line correctly identifies the equation and named variables for work done when moving a mass in a gravitational field?

  symbol equation word equation
A. Fs force × distance
B. FΔV force × change in gravitational potential
C. ms mass × distance
D. mΔV mass × change in gravitational potential

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    15
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    When a mass moves through a gravitational field the magnitude of the potential energy EP  changes. Which equation could be used to correctly calculate this?

    • increment E subscript p equals G M m open parentheses 1 over r subscript 1 minus 1 over r subscript 2 close parentheses

    • increment E subscript p equals G M m open parentheses negative 1 over r subscript 1 minus 1 over r subscript 2 close parentheses

    • increment E subscript p equals G M m open parentheses 1 over r subscript 1 plus 1 over r subscript 2 close parentheses

    • increment E subscript p equals G M m open parentheses 1 over r subscript 1 cross times 1 over r subscript 2 close parentheses

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    16
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    Read the following statements about the escape velocity on Earth. Which ones are correct?

    Escape velocity;

    1. Increases as the mass of the object increases
    2. Depends on the mass of the Earth and is not affected by the mass of the object
    3. Is defined as the minimum speed that allows an object to escape a gravitational field with no further energy input

    • I. only

    • I. and II.

    • II. and III.

    • III. only

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    17
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    The equation for linear orbital speed is

    v equals square root of fraction numerator G M over denominator r end fraction end root

    Which statement is a consequence of this equation?

    • Orbital speed is the same for all objects, regardless of their mass, when their orbital radius is the same.

    • Orbital speed is the same for all objects, regardless of their mass, when they orbit the same planet.

    • The gravitational constant, G, can be derived if orbital speed and radius are both known.

    • Time period, T can be derived from orbital speed and radius.

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    1
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    The gravitational force between two identical uniform spheres of mass M is F when the distance between them d.

    q14_newtons-law-of-gravitation_ib-sl-physics-mcq

    If the radius of each sphere is x, what is the correct expression for mass, M?

    • fraction numerator straight F left parenthesis d plus 2 x right parenthesis squared over denominator straight G end fraction

    • square root of fraction numerator straight F d squared over denominator straight G end fraction end root

    • square root of fraction numerator straight F left parenthesis d plus 2 x right parenthesis over denominator straight G end fraction end root

    • square root of fraction numerator straight F left parenthesis d plus 2 x right parenthesis squared over denominator straight G end fraction end root

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    2
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    A satellite of mass m is placed in a geostationary orbit. If the Earth’s angular velocity is ω rad s–1, what is the circumference of the satellite’s orbit?

    • open parentheses fraction numerator G M over denominator omega squared end fraction close parentheses to the power of 1 third end exponent

    • 2 straight pi square root of GMm over straight omega squared end root

    • 2 straight pi open parentheses fraction numerator G M over denominator straight omega squared end fraction close parentheses

    • 2 straight pi open parentheses fraction numerator G M over denominator straight omega squared end fraction close parentheses to the power of 1 third end exponent

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    3
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    A spherical planet of uniform density has two times the mass of the Earth and three times the average radius. The magnitude of the gravitational field strength at the surface of the Earth is g. What is the gravitational field strength at the surface of the planet?

    • 3 over 4 g

    • 2 over 3 g

    • 2 over 9 g

    • 18g

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    4
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    The inverse square law means that halving the radius of a planet results in quadrupling the gravitational field strength at its surface.

    The centres of two planets are separated by a distance R. The gravitational force between the two planets is F. What will the force between the planets be when their separation increases to 4R?

    • F over 16

    • 4F

    • F over 4

    • F

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    5
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    A mass at point P gives rise to a gravitational field strength g at point X as shown.

    q18_1_newtons-law-of-gravitation_ib-sl-physics-mcq

    An identical mass is placed at point Q as shown.

    q18_2_newtons-law-of-gravitation_ib-sl-physics-mcq

    What is the resultant gravitational field strength at X in this new situation?

    • zero

    • between g and zero

    • between 2g and g 

    • greater than 2g

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    6
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    A spacecraft travels away from Earth in a straight line with its motors shut down. At one instant, the speed of the spacecraft is 5.7 km s-1. After a time of 1000 s, the speed is 5.2 km s-1.

    What is the gravitational field strength acting on the spacecraft during this time interval?

    • –5 × 10–4 N kg–1

    • 5 × 101 N kg–1

    • –5 × 10–1 N kg–1

    • –1 × 101 N kg–1

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    7
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    Which of the following statements about uniform gravitational fields is incorrect?

    • The field strength is equal at every point in a uniform gravitational field

    • The acceleration of freefalling bodies is dependent on their mass

    • The field lines in a uniform gravitational field are parallel to each other  

    • There is a uniform gravitational field near the Earth’s surface

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    8
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    A test mass m moves between position A and B as shown, in the presence of a source mass M. 

    10-1-hl-mcq-medium-q1

    Which of the following statements is correct? 

    • Negative work is done on m by the gravitational field from A to B

    • The gravitational field of M does negative work on m

    • m moves along an equipotential

    • The gravitational field of M does work on m

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    9
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    A positive charge Q is deposited on the surface of a small sphere. The dotted lines represent equipotentials.

    10-1-hl-mcq-medium-q3

    A small positive point charge is moved from point P closer to the sphere along two different paths X and Y. What is the best comparison of the work done along X and Y, WX and WY?

    • WX = WY

    • WX < WY

    • WX > WY

    • WX ≈ WY

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    10
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    Equipotential surfaces corresponding to lines of constant gravitational potential are conventionally drawn so that the difference in potential between any two adjacent surfaces is the same. 

    Consider the equipotential surfaces for a spherical mass M. Which of the following statements is incorrect? 

    • Equipotential surfaces are spheres of constant radius around M

    • The distance between equipotential surfaces increases with distance from M

    • No work is done by the gravitational field of M if a test mass moves along an equipotential surface

    • The radius of each equipotential surface depends on the diameter of M

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    11
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    Which of the following statements about gravitational fields is correct?

    • The gravitational potential is zero whenever the gravitational field strength is zero

    • The gravitational potential is negative because the gravitational field is repulsive

    • The gradient of the gravitational potential at a point is inversely proportional to the radial distance from some massive body

    • The area under a field strength–distance curve represents the change in gravitational potential between two points

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    12
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    The mass of Jupiter is mJ and the mass of its moon Europa is mE. 

    If their radii is given by rJ and rE respectively, what is the ratio fraction numerator e s c a p e space v e l o c i t y space o f space E u r o p a over denominator e s c a p e space v e l o c i t y space o f space J u p i t e r end fraction?

    • square root of fraction numerator m subscript E space space r subscript E over denominator m subscript J space space r subscript J end fraction end root

    • square root of fraction numerator m subscript E space space r subscript J over denominator m subscript J space space r subscript E end fraction end root

    • square root of fraction numerator m subscript J space space r subscript J over denominator m subscript E space space end subscript r subscript E end fraction end root

    • square root of fraction numerator m subscript J space space r subscript E over denominator m subscript E space space end subscript r subscript J end fraction end root

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    13
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    A satellite of mass 2000 kg is in the Earth’s gravitational field. It moves radially from a point where the gravitational potential is –40 MJ kg–1 to a point where the gravitational potential is –10 MJ kg–1. What is the direction of movement of the satellite and the change in its gravitational potential energy?

     

    Direction of movement of satellite

    Change in gravitational potential energy / GJ

    A.

    Parallel to a field line

    60

    B.

    Antiparallel to a field line

    30

    C.

    Along an equipotential

    30

    D.

    Antiparallel to a field line

    60

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      14
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      Which graph shows how the kinetic energy EK, the potential energy EP and the total energy E of the international space station varies with distance x from the centre of Earth?

      10-2-hl-mcq-medium-q3

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        15
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        A probe is launched from the surface of the Earth, which has a radius R, at half the required escape velocity. 

        What is the maximum height from the surface the probe will reach, before returning to the ground (with a bang)? 

        • R

        • R over 2

        • R over 3

        • R over 4

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        16
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        The graph shows the variation of gravitational potential V with distance r from the centre of a spherical planet of mass M and radius R0. 

        10-2-hl-mcq-medium-q6

        Which statement best describes how to determine the gravitational field strength at a distance r = R from the planet?

        • The area enclosed by the horizontal axis, the line r = R0, the line r = R, and the curve 

        • The gradient at the point r = R

        • The inverse of the gradient at the point r = R

        • The negative of the gradient at the point r = R

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        17
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        The gravitational field strength is g and the gravitational potential is V at the surface of Earth, which has a radius of r.  

        Which row in the table gives the correct value of the gravitational field strength and the gravitational potential at a height of 2r from Earth's surface? 

         

        Gravitational field strength

        Gravitational potential

        A.

        g over 3

        V over 3

        B.

        g over 4

        V over 2

        C.

        g over 9

        V over 3

        D.

        g over 16

        V over 2

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          1
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          The shape of equipotential surfaces in the gravitational field depends on perspective. 

          The image below shows equipotential surfaces (represented by dotted lines) due to the Earth’s gravitational field in a ‘local’ frame of reference (close to the Earth’s surface) and in a ‘non–local’ frame of reference (far from the Earth’s surface):

          qu15-intro

          Which line, A to D, in the table shows the variation of gravitational potential V with radial distance r from the Earth’s surface?

          You may assume each dotted line represents equal changes in potential ΔV and that rE represents the radius of the Earth.

           

          • qu15a-

          • qu15b

          • qu15c

          • qu15d

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          2
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          The relative positions of a binary star system is shown below:

          qu14-intro

          The line XY joins the surface of the star of mass m to the surface of the star of mass M > m. Assume the stars have the same diameter.

          Which graph correctly represents the variation of the gravitational potential ϕ along the line XY? 

          qu14

           

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            3
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            Planet Z, with centre O, is shown in the figure below.

            qu11

            The radial distances OP is equal to the OX, and OQ is equal to OY, such that PX and QY are loci of Planet Z.

            Which of the following statements is incorrect?

            • The work done by the gravitational field on a test mass moving from P to Q is negative

            • The gravitational field does zero work on a test mass moving along the locus PX

            • V subscript X over V subscript Q equals fraction numerator O Y over denominator O X end fraction

            • The work done by an external force to move a test mass from Y to X is positive

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            4
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            Two objects X and Y of equal mass, m and distance, D apart move with a constant speed v in circular orbit about their common centre of mass CM. X has a charge of +6.0 nC and Y has a charge of –6.0 nC.

            10-1-ib-hl-mcq-q8

            Which graphs shows the electric potential, V and gravitational potential, φ,  against position along the straight-line joining X and Y?

            10-1-ib-hl-mcq-q8-2

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              5
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              The Earth has radius, r and mass M. Which expression could be used to calculate the minimum time, T of one Earth-day for the material at the equator to just remain on the surface?

              • fraction numerator 4 pi squared space m r over denominator G M end fraction

              • fraction numerator 2 pi space r cubed over denominator G M end fraction

              • fraction numerator 4 pi squared space r cubed over denominator G M end fraction

              • 2 pi square root of fraction numerator r cubed over denominator G M end fraction end root

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              6
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              A space probe with mass m is launched from the surface of the Earth’s equator into orbit. The total energy Et given to the space probe is:

              E subscript t equals fraction numerator 3 G M m over denominator 4 space r subscript E end fraction

              where G is the gravitational constant and M and rE are the mass and radius of Earth.

              What is the height of the space probe’s orbit above the Earth’s surface?

              • rE

              • 2rE

              • 3rE

              • 4rE

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              7
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              Two satellites, X and Y, of equal mass, orbit a planet at radii R and 2R respectively.

              Which one of the following statements is correct?

              • X has more kinetic energy and more potential energy than Y

              • X has more kinetic energy and less potential energy than Y

              • X has less kinetic energy and more potential energy than Y

              • X has less kinetic energy and less potential energy than Y

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              8
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              Observations are made on two separate planetary system's suns of mass M1 and mass M2.

              Their orbiting planets, P1 and P2 have masses of m1 and m2, and are observed to have identical orbits in shape and magnitude. P1 completes an orbit in a quarter of the time taken by P2.

              Which statement can astronomers reasonably deduce?

              • M1 = M2 and 9m1 = m2

              • M1 = 16 M2 and m1 = m2

              • 4 M1 = M2 

              • M1 = 16 M2 

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