Density = 2 a a CF, J.7) Figure 16.75
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Question
Center of mass with variable density Find the center of mass of the
interior of the hemisphere D of radius a with its base on the xy-plane. The density of the object given in spherical coordinates is ƒ(ρ, φ, θ) = 2 - ρ/a (heavy near the center and light near the outer surface; as shown).
Expert Solution
Step 1
Given Data:
- The density of the hemisphere is given as
To determine the centre of mass of the hemisphere, take a hemispherical shell of radius and thickness . The centre of mass of this spherical shell has coordinate as shown in the figure.
Step 2
The mass dm of the spherical shell can be determined as,
The expression for the location of the centre of mass is,
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