![James Stewart Calculus for MAT 127/128/229 8th edition](https://www.bartleby.com/isbn_cover_images/9781305743663/9781305743663_largeCoverImage.gif)
Concept explainers
Assume that the earth is a solid sphere of uniform density with mass M and radius R = 3960 mi. For a particle of mass m within the earth at a distance r from the earth’s center, the gravitational force attracting the particle to the center is
(a) Show that
(b) Suppose a hole is drilled through the earth along a diameter. Show that if a particle of mass m is dropped from rest at the surface, into the hole, then the distance y = y(t) of the particle from the center of the earth at time t is given by y"(t) = -k2y(t)
where k2 = GM/R3 = g/R.
(c) Conclude from part (b) that the particle undergoes simple harmonic motion. Find the period T.
(d) With what speed does the particle pass through the center of the earth?
![Check Mark](/static/check-mark.png)
Want to see the full answer?
Check out a sample textbook solution![Blurred answer](/static/blurred-answer.jpg)
Chapter 17 Solutions
James Stewart Calculus for MAT 127/128/229 8th edition
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
![Text book image](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781337278461/9781337278461_smallCoverImage.gif)