# 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?