A thick spherical shell occupies the region between two spheres of radii a and 2a, both centred on the origin. The shell is made of a material with density p = A(x² + y2) z², where A is a constant. (a) Show that the density expressed in spherical coordinates (r, 0, 0) is p= Ar¹(1-cos²0) cos² 0. (b) Hence, or otherwise, find the mass of the shell by evaluating a suitable volume integral. Hint: You may find the substitution u = cos useful.
A thick spherical shell occupies the region between two spheres of radii a and 2a, both centred on the origin. The shell is made of a material with density p = A(x² + y2) z², where A is a constant. (a) Show that the density expressed in spherical coordinates (r, 0, 0) is p= Ar¹(1-cos²0) cos² 0. (b) Hence, or otherwise, find the mass of the shell by evaluating a suitable volume integral. Hint: You may find the substitution u = cos useful.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A thick spherical shell occupies the region between two spheres of radii a
and 2a, both centred on the origin. The shell is made of a material with
density p = A(x² + y2) z², where A is a constant.
(a) Show that the density expressed in spherical coordinates (r, 0, 0) is
p= Ar¹(1 cos²0) cos² 0.
(b) Hence, or otherwise, find the mass of the shell by evaluating a suitable
volume integral.
Hint: You may find the substitution u = = cos useful.
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