Explanation Due to the symmetry of the bodies the center of mass has only coordinate in the Z direction. Now, by the volume integral. Z C = 1 v ∫ z d v = ∭ d x d y d z The spherical coordinates are as, x = r sin ϕ cos θ y = r sin ϕ sin θ z = r cos ϕ Thus, Z C = 1 v ∭ r cos ϕ r 2 sin ϕ d r d ϕ d θ = 1 2 v ∭ r 2 sin 2 θ d r d ϕ d θ Now, the solid hemisphere with the radius R has volume, Z C = 3 4

Mathematical Methods in the Physical Sciences

3rd Edition

ISBN: 9780471198260

Author: Mary L. Boas

Publisher: Wiley, John & Sons, Incorporated

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Chapter 5.4, Problem 28P

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To find: The center of mass of a hemispherical shell of constant shell using double integral and area element dA .

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Chapter 5.4, Problem 27P

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Chapter 5 Solutions

Mathematical Methods in the Physical Sciences

Ch. 5.1 - 2sincocd=sin2or-cos2or-12cos2. Hint: Use trig...Ch. 5.1 - dxx2+a2=sinh1xaorInx+x2+a2. Hint:To find the sinh1...Ch. 5.1 - dyy2a2=cosh1yaorIny+y2a2. Hint: See Problem 2...Ch. 5.1 - ...Ch. 5.1 - Kdr1k2r2=sinh1Kror-cos1Krortan1Kr1k2r2 Hints:...Ch. 5.1 - Kdrrr2k2cos1krorsec1rkor-sin1kror-tan1Kr2k2 Ch. 5.2 - In the problems of this section, set up and...Ch. 5.2 - In the problems of this section, set up and...Ch. 5.2 - In the problems of this section, set up and...Ch. 5.2 - In the problems of this section, set up and...

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The center of mass of a hemispherical shell of constant shell using double integral and area element d A .

Solution Summary: The author explains the center of mass of a hemispherical shell of constant shell using double integral and area element dA.

To find: The center of mass of a hemispherical shell of constant shell using double integral and area element dA .

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Chapter 5 Solutions