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AP®PhysicsCollege BoardPhysics 1: Algebra-BasedExam QuestionsUnit 2: Force & Translational DynamicsGravitational Force

Gravitational Force (College Board AP® Physics 1: Algebra-Based): Exam Questions

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11 mark

Two artificial satellites are in orbit around the Earth. The first has a mass of 3.2 space cross times space 10 to the power of 5 space kg and orbits at a height of 3 space km above the Earth's surface. The second has a mass of 1.6 space cross times space 10 to the power of 6 space kg and orbits at a height of 5 space km above the surface of the Earth.

Which of the following is the best estimate of the ratio of the gravitational force between each satellite and the Earth?

  • 0.035

  • 0.33

  • 0.56

  • 2.78

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2
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A silver ball bearing, suspended on a newtonmeter, is lowered into a beaker of water. The newtonmeter shows the weight of the ball bearing to be 4 space straight Nwhen in air and floating on the surface of the water in the beaker and it shows the weight to be 1 space straight Nwhen it is fully submerged.

Which option is the best estimate of the magnitude of the buoyant force acting on the ball bearing due to the water in the beaker when it is fully submerged?

Diagram showing a spring balance measuring a sphere's weight in air, partially and fully submerged in liquid-filled beakers with overflow measurement.

  • 1 space straight N

  • 3 space straight N

  • 4 space straight N

  • 5 space straight N

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3
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Which of the following best describes Newton's law of universal gravitation?

  • The gravitational force between two objects or systems is directly proportional to each of their masses and inversely proportional to the square of the distance between the systems’ centers of mass.

  • The gravitational force between two objects or systems is inversely proportional to each of their masses and directly proportional to the square of the distance between the systems’ centers of mass.

  • The gravitational force between two objects or systems is directly proportional to the square of each of their masses and inversely proportional to the distance between the systems’ centers of mass.

  • The gravitational force between two objects or systems is inversly proportional to the square of each of their masses and directly proportional to the distance between the systems’ centers of mass.

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4
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Which of the following is correct for the gravitational force?

  • The gravitational force can be attractive or repulsive.

  • The gravitational force is always exerted along the line connecting the centers of mass of the two interacting systems.

  • The gravitational force on a system can be considered to be exerted from the midpoint between the centers of mass of the objects that make up the system.

  • The gravitational force can always be considered constant at all points between the initial and final positions of the systems.

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5
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How does the mass of an object affect its acceleration during free fall in a vacuum?

  • More massive objects accelerate faster.

  • Less massive objects accelerate faster.

  • Objects accelerate equally regardless of mass.

  • Acceleration depends on the physical shape of the object.

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1
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Europa is one of Jupiter's natural satellites which orbits at a height of 670 space 000 space km above Jupiter's surface. The mass of Jupiter is 2 space cross times space 10 to the power of 27 space kg and it's radius is 70 space 000 space km. The gravitational force between Jupiter and Europa is 1.5 space cross times space 10 to the power of 22 space straight N.

Which of the following is the mass of Europa when it is modelled as a point mass in this scenario?

  • 8 space cross times space 10 to the power of 13 space kg

  • 6 space cross times space 10 to the power of 14 space kg

  • 5 space cross times space 10 to the power of 16 space kg

  • 6 space cross times space 10 to the power of 22 space kg

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2
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A planet has twice the mass of Earth but only two-thirds the radius. What would be the magnitude of the gravitational field strength on this planet compared to Earth?

  • Same as Earth.

  • Twice that of Earth.

  • Three times that of Earth.

  • Four and a half times as much as Earth.

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3
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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, which of the following is the correct expression for mass, M?

  • fraction numerator open vertical bar F with rightwards arrow on top subscript g close vertical bar open parentheses d plus 2 x close parentheses squared over denominator G end fraction

  • square root of fraction numerator open vertical bar F with rightwards arrow on top subscript g close vertical bar d squared over denominator G end fraction end root

  • square root of fraction numerator open vertical bar F with rightwards arrow on top subscript g close vertical bar open parentheses d plus 2 x close parentheses over denominator G end fraction end root

  • square root of fraction numerator open vertical bar F with rightwards arrow on top subscript g close vertical bar open parentheses d plus 2 x close parentheses squared over denominator G end fraction end root

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41 mark

A person has a weight of 765 space straight N on Earth. Which of the following is their correct weight on a planet with a mass 4.5 times that of Earth and a radius 1.8 times that of Earth?

  • 675 space straight N

  • 924 space straight N

  • 1063 space straight N

  • 1238 space straight N

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5
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An astronaut of mass 70 space kgis in a spacecraft of mass 9.2 cross times 10 to the power of 5 space kg orbiting Earth at an altitude where the gravitational field strength is 7.3 space straight N divided by kg. The spacecraft accelerates from rest at 1.5 space straight m divided by straight s squared upward.

Which of the following is the apparent weight of the astronaut?

  • 406 space straight N

  • 616 space straight N

  • 805 space straight N

  • 1.4 cross times 10 to the power of 6 space straight N

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11 mark

An experiment with a mass set to oscillate on a spring is set up on another planet where the gravitational field strength is 4 space straight N divided by kg. The radius of the planet is 590 space km.

Which of the following values is the closest to the mass of the planet?

  • 1 space cross times space 10 to the power of negative 7 end exponent space kg

  • 2 space cross times space 10 to the power of negative 4 end exponent space kg

  • 4 space cross times space 10 to the power of 16 space kg

  • 2 space cross times space 10 to the power of 22 space kg

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2
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A person of mass 50 space kg is standing on a bathroom scale on the floor of an elevator holding a ball. The cable holding the elevator in position snaps and the elevator falls to the ground. The person lets go of the ball.

Which of the following shows the correct statements about the person and the ball as the elevator falls to the ground?

  • Person

    Ball

    the scale reads zero

    the ball remains in the same position in the air

  • Person

    Ball

    the scale reads 50 space kg

    the ball falls to the floor of the elevator

  • Person

    Ball

    the scale reads zero

    the ball rises to the ceiling of the elevator

  • Person

    Ball

    the scale reads 500 space straight N

    the ball remains in the same position in the air

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3
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A person of mass 60 space kg stands on a scale in an elevator that is accelerating. The scale reads 720 space straight N.

Which of the following correctly describes the motion of the elevator?

  • Accelerating upward at 2 space straight m divided by straight s squared

  • Accelerating upward at 22 space straight m divided by straight s squared

  • Accelerating downward at 2 space straight m divided by straight s squared

  • Accelerating downward at 22 space straight m divided by straight s squared

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4
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A person of mass 72 space kg is in an elevator travelling downwards.

At the start of the journey, the elevator accelerates with a magnitude 2.3 space straight m divided by straight s squared. At the end of the journey, the elevator decelerates with a magnitude 2.3 space straight m divided by straight s squared.

What is the ratio of the person's apparent weight at the start of the journey to the person's apparent weight at the end of the journey?

  • 1.4

  • 1.5

  • 1.6

  • 1.7

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51 mark

Observations are made on two separate planetary system's stars of mass M subscript 1 and mass M subscript 2.

Their orbiting planets, P subscript 1 and P subscript 2 have masses of m subscript 1 and m subscript 2, and are observed to have identical orbits in shape and radius. P subscript 1 completes an orbit in a quarter of the time taken by P subscript 2.

Which of the following statements can astronomers reasonably deduce?

  • M subscript 1 space equals space M subscript 2 and 9 m subscript 1 space equals space m subscript 2

  • M subscript 1 space equals space 16 M subscript 2 and m subscript 1 space equals space m subscript 2

  • 4 M subscript 1 space equals space M subscript 2

  • M subscript 1 space equals space 16 M subscript 2

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