Worksheet: The Gravitational Field Inside Planets

In this worksheet, we will practice calculating the magnitude of the acceleration due to gravity at a point inside of a planet.

Q1:

Which of the following relations shows how the local acceleration due to gravity, π‘Ž, at any point outside or inside a planet varies with the density of the planet, 𝜌, if the planet has a constant density throughout?

  • Aπ‘ŽβˆπœŒοŠ©
  • Bπ‘ŽβˆπœŒοŠ¨
  • Cπ‘Žβˆ1𝜌
  • Dπ‘Žβˆ1𝜌
  • Eπ‘ŽβˆπœŒ

Q2:

What is the acceleration due to gravity at a distance of 0.15 π‘…οŒ€ from Earth’s center of mass? Assume that Earth is a perfect sphere with a radius 𝑅=6,370 km and a constant density of 5,510 kg/m3. Give your answer to 3 significant figures.

Q3:

What is the acceleration due to gravity at the center of Earth?

Q4:

What is the acceleration due to gravity at a distance from Earth’s center of mass that is equal to half the Earth’s radius? Assume that Earth is a perfect sphere with a radius of 6,370 km and a constant density of 5,510 kg/m3. Give your answer to 3 significant figures.

Q5:

The figure shows how the acceleration due to gravity inside and outside of a planet varies along two spatial dimensions. The planet has a constant density. At which of the five points shown in the figure is the acceleration due to gravity zero?

  • APoint C
  • BPoint B
  • CPoint E
  • DPoint A
  • EPoint D

Q6:

The graph shows how the acceleration due to gravity inside and outside of Earth varies with radial distance away from the Earth’s center of mass. Earth is assumed to be a perfect sphere of constant density.

Which of the following relations describes the shape of the graph in region A?

  • Aπ‘Žβˆπ‘ŸοŠ¨
  • Bπ‘Žβˆ1π‘ŸοŠ¨
  • Cπ‘Žβˆπ‘Ÿ
  • Dπ‘Žβˆ1π‘Ÿ
  • Eπ‘Žβˆβˆš(π‘Ÿ)

Which of the following relations describes the shape of the graph in region B?

  • Aπ‘Žβˆ1π‘ŸοŠ¨
  • Bπ‘Žβˆπ‘Ÿ
  • Cπ‘Žβˆ1π‘Ÿ
  • Dπ‘Žβˆπ‘ŸοŠ¨
  • Eπ‘Žβˆβˆš(π‘Ÿ)

Q7:

The graph shows how the acceleration due to gravity varies with radial distance inside and outside of three planets. Each planet is a perfect sphere and has a constant density.

Which of the following statements is true about all of the planets?

  • AAll of the planets have the same surface gravity.
  • BAll of the planets have the same radius.
  • CAll of the planets have the same volume.
  • DAll of the planets have the same mass.
  • EAll of the planets have the same density.

Which planet has the largest radius?

  • AThey all have the same radius.
  • BPlanet B
  • CPlanet A
  • DPlanet C

Q8:

The graph shows how the acceleration due to gravity varies with radial distance inside and outside of three planets. Each planet is a perfect sphere and has a constant density.

Which of the following statements is true about all of the planets?

  • AAll of the planets have the same radius.
  • BAll of the planets have the same density.
  • CAll of the planets have the same surface gravity.
  • DAll of the planets have the same mass.

Which planet has the greatest density?

  • APlanet C
  • BPlanet B
  • CPlanet A
  • DThey all have the same density.

Q9:

Which of the following relations shows how the local acceleration due to gravity, π‘Ž, varies with the radial distance, π‘Ÿ, from Earth’s center of mass within Earth? Assume that Earth is a perfect sphere with constant density.

  • Aπ‘Žβˆ1π‘ŸοŠ¨
  • Bπ‘Žβˆπ‘Ÿ
  • Cπ‘Žβˆ1π‘Ÿ
  • Dπ‘Žβˆπ‘ŸοŠ©
  • Eπ‘Žβˆπ‘ŸοŠ¨

Q10:

The figure shows how the acceleration due to gravity inside and outside of a planet varies along two spatial dimensions. The planet has a constant density. At which of the five points shown in the figure is the acceleration due to gravity greatest?

  • APoint A
  • BPoint D
  • CPoint C
  • DPoint B
  • EPoint E

Q11:

The acceleration due to gravity on the surface of Earth is 9.81 m/s2. If the radius of Earth were double its actual value but its average density remained the same, what would Earth’s surface gravity be?

Q12:

The graph shows how the acceleration due to gravity inside and outside of a planet varies with radial distance away from the planet’s center of mass.

If the planet is a perfect sphere of constant density, what is the radius of the planet?

Q13:

The figure shows how the acceleration due to gravity inside and outside of a planet varies along two spatial dimensions. The planet has a constant density. At which of the five points shown in the figure is the acceleration due to gravity smallest?

  • APoint D
  • BPoint E
  • CPoint C
  • DPoint A
  • EPoint B

Q14:

The figure shows the acceleration due to gravity along two spatial dimensions in a region of space. The curvature of the surface reveals the gravitational effect of two planets, A and B. The planets each have constant densities and the same radius. Which of the two planets has a lower density?

  • APlanet A
  • BPlanet B

Q15:

The figure shows the acceleration due to gravity along two spatial dimensions in a region of space. The curvature of the surface reveals the gravitational effect of two planets, A and B. The planets have constant densities. Which of the two planets has the larger radius?

  • APlanet A
  • BPlanet B

Q16:

The graph shows how the acceleration due to gravity varies with radial distance inside and outside of three planets. Each planet is a perfect sphere and has a constant density.

Which planet has the greatest density?

  • APlanet C
  • BPlanet B
  • CPlanet A
  • DThey all have the same density.

Which planet has the largest radius?

  • AThey all have the same radius.
  • BPlanet B
  • CPlanet C
  • DPlanet A

Which planet has the greatest surface gravity?

  • APlanet B
  • BPlanet A
  • CThey all have the same surface gravity.
  • DPlanet C

Q17:

The figure shows how the acceleration due to gravity inside and outside of a planet varies along two spatial dimensions. The planet has a constant density.

Which of the five points shown in the figure marks a point on the surface of the planet?

  • APoint E
  • BPoint D
  • CPoint B
  • DPoint A
  • EPoint C

Which of the five points shown in the figure marks the center of the planet?

  • APoint B
  • BPoint A
  • CPoint D
  • DPoint E
  • EPoint C

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