# 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 Earthβs center of mass? Assume that Earth is a perfect sphere with a radius
km
and a constant density of 5,510 kg/m^{3}.
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 Earthβs
center of mass that is equal to half the Earthβs radius?
Assume that Earth is a perfect sphere with a radius of 6,370 km
and a constant density of 5,510 kg/m^{3}.
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 Earthβs 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 Earthβs 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/s^{2}.
If the radius of Earth were double its actual value but its average density
remained the same, what would Earthβs 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 planetβs 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