# 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, , at any point outside or inside a planet varies with the density of the planet, , if the planet has a constant density throughout?

• A
• B
• C
• D
• E

Q2:

What is the acceleration due to gravity at a distance of 0.15 from Earth’s center of mass? Assume that Earth is a perfect sphere with a radius 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?

• A
• B
• C
• D
• E

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

• A
• B
• C
• D
• E

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, , varies with the radial distance, , from Earth’s center of mass within Earth? Assume that Earth is a perfect sphere with constant density.

• A
• B
• C
• D
• E

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