Worksheet: Newton's Law of Gravitation

In this worksheet, we will practice using Newton's Law of Gravitation to calculate the force due to gravity between two massive objects.

Q1:

Earth has a mass of 5 . 9 7 × 1 0 kg, and the Moon has a mass of 7 . 3 4 × 1 0 kg. The average distance between the center of Earth and the center of the Moon is 384,000 km. What is the magnitude of the gravitational force between Earth and the Moon? Use a value of 6 . 6 7 × 1 0 m3/kg⋅s2 for the universal gravitational constant. Give your answer to 3 significant figures.

  • A 2 . 7 3 × 1 0 N
  • B 1 . 9 8 × 1 0 N
  • C 1 . 9 8 × 1 0 N
  • D 7 . 6 1 × 1 0 N
  • E 7 . 6 1 × 1 0 N

Q2:

Two spaceships are in deep space. The distance between the centers of mass of the two spaceships is 300 m, and the force between them is 5 . 5 1 × 1 0 N. If one spaceship has a mass of 24,000 kg, what is the mass of the other spaceship? Use a value of 6 . 6 7 × 1 0 m3/kg⋅s2 for the universal gravitational constant. Give your answer to 3 significant figures.

Q3:

A man, who is standing on the surface of Earth, has a mass of 72 kg. Earth has a mass of 5 . 9 7 × 1 0 kg and a radius of 6,370 km. What is the magnitude of the gravitational force between the man and Earth? Use a value of 6 . 6 7 × 1 0 m3/kg⋅s2 for the universal gravitational constant. Give your answer to 3 significant figures.

Q4:

Titan is the largest moon of Saturn. It has a mass of 1 . 3 5 × 1 0 kg. Saturn has a mass of 5 . 6 8 × 1 0 kg. If the magnitude of the gravitational force between them is 3 . 4 3 × 1 0 N, what is the distance between the centers of mass of Saturn and Titan? Use a value of 6 . 6 7 × 1 0 m3/kg⋅s2 for the universal gravitational constant. Give your answer to 3 significant figures.

  • A 1 . 4 9 × 1 0 m
  • B 2 . 0 9 × 1 0 m
  • C 1 . 2 2 × 1 0 m
  • D 1 . 7 5 × 1 0 m
  • E 3 . 3 2 × 1 0 m

Q5:

Which of the following is the correct formula for Newton’s law of gravitation?

  • A 𝐹 = 𝐺 𝑚 𝑚 𝑟
  • B 𝐹 = 𝐺 ( 𝑚 + 𝑚 ) 𝑟
  • C 𝐹 = 𝐺 𝑚 𝑚 𝑟
  • D 𝐹 = 𝐺 ( 𝑚 + 𝑚 ) 𝑟
  • E 𝐹 = 𝐺 𝑚 𝑚 𝑟

Q6:

Two asteroids, 𝐴 and 𝐵 , are in deep space. Asteroid 𝐴 has a mass of 5 . 7 5 × 1 0 kg, and asteroid 𝐵 has a mass of 1 . 3 9 × 1 0 kg. If the magnitude of the gravitational force between them is 0.370 N, what is the distance between the centers of mass of the two asteroids? Use a value of 6 . 6 7 × 1 0 m3/kg⋅s2 for the universal gravitational constant. Give your answer to 3 significant figures.

Q7:

Two objects, 𝐴 and 𝐵 , are in deep space. Object 𝐴 has a mass of 15,000 kg and object 𝐵 has a mass of 26,000 kg. The distance between the centers of mass of the two objects is 25 m. What is the acceleration of object 𝐵 towards object 𝐴 due to their gravitational interaction? Use a value of 6 . 6 7 × 1 0 m3/kg⋅s2 for the universal gravitational constant. Give your answer to 3 significant figures.

  • A 1 . 6 0 × 1 0 m/s2
  • B 4 . 1 6 × 1 0 m/s2
  • C 2 . 7 7 × 1 0 m/s2
  • D 6 . 9 4 × 1 0 m/s2
  • E 4 . 0 0 × 1 0 m/s2

Q8:

Which of the following relations shows how the magnitude of the gravitational force between two objects, 𝐹 , varies with the masses of the two objects, 𝑚 and 𝑚 ?

  • A 𝐹 𝑚 + 𝑚
  • B 𝐹 𝑚 𝑚
  • C 𝐹 𝑚 𝑚
  • D 𝐹 𝑚 × 𝑚
  • E 𝐹 𝑚 𝑚

Q9:

The figure shows two large rocks in outer space. Each rock has a mass of 480 kg. What is the magnitude of the gravitational force between the two rocks? Use a value of 6 . 6 7 × 1 0 m3/kg⋅s2 for the universal gravitational constant. Give your answer to 3 significant figures. The grid lines on the grid are spaced 1 m apart.

  • A 3 . 2 0 × 1 0 N
  • B 3 . 2 0 × 1 0 N
  • C 1 . 5 4 × 1 0 N
  • D 1 . 7 1 × 1 0 N
  • E 1 . 5 4 × 1 0 N

Q10:

The figure shows two large rocks in outer space. Each rock has a mass of 150 kg. What is the magnitude of the gravitational force between the two rocks? Use a value of 6 . 6 7 × 1 0 m3/kg⋅s2 for the universal gravitational constant. Give your answer to 3 significant figures. The grid lines on the grid are spaced 1 m apart.

  • A 3 . 7 5 × 1 0 N
  • B 7 . 5 0 × 1 0 N
  • C 1 . 6 7 × 1 0 N
  • D 5 . 0 0 × 1 0 N
  • E 2 . 5 0 × 1 0 N

Q11:

Earth has a mass of 5 . 9 7 × 1 0 kg and orbits the Sun at a distance of 1 . 5 0 × 1 0 m. The magnitude of the gravitational force between Earth and the Sun is 3 . 5 4 × 1 0 N. What is the mass of the Sun? Use a value of 6 . 6 7 × 1 0 m3/kg⋅s2 for the universal gravitational constant. Give your answer to 3 significant figures.

  • A 2 . 0 0 × 1 0 kg
  • B 3 . 3 7 × 1 0 kg
  • C 2 . 2 1 × 1 0 kg
  • D 1 . 3 3 × 1 0 kg
  • E 5 . 6 9 × 1 0 kg

Q12:

Which of the lines on the graph shows how the magnitude of the gravitational force between two objects varies with the distance between their centers of mass?

  • AThe purple line
  • BThe red line
  • CThe blue line
  • DThe black line
  • EThe green line

Q13:

The figure shows two large rocks in outer space. One rock has a mass of 500 kg; the other has a mass of 800 kg. What is the magnitude of the gravitational force between the two rocks? Use a value of 6 . 6 7 × 1 0 m3/kg⋅s2 for the universal gravitational constant. Give your answer to 3 significant figures. The grid lines on the grid are spaced 1 m apart.

  • A 4 . 4 5 × 1 0 N
  • B 7 . 4 1 × 1 0 N
  • C 1 . 0 7 × 1 0 N
  • D 1 . 0 3 × 1 0 N
  • E 3 . 9 5 × 1 0 N

Q14:

Which of the following relations shows how the magnitude of the gravitational force between two objects, 𝐹 , varies with the distance between their centers of mass, 𝑟 ?

  • A 𝐹 1 𝑟
  • B 𝐹 𝑟
  • C 𝐹 1 𝑟
  • D 𝐹 𝑟
  • E 𝐹 1 𝑟

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