Explanation Given: p ( r ) = 0.03 + 0.01 cos ( π r 2 ) g / c m 2 Calculation: We have been given that, radius of circular plate = 20 cm and mass density = p ( r ) = 0.03 + 0.01 cos ( π r 2 ) g / c m 2 To calculate the mass of circular plate, thin rings inside the circle are considered, as shown below, Now, if we straightened out each ring we get rectangular strips, with length as the circumference of that ring 2πr (r is radius of the ring) and breadth as the difference in radius dr Therefore, area of ring = 2πr*dr square cm Therefore, mass of ring = area of ring* mass density Therefore, total mass, M in g= sum of (area of ring*mass density) = integral of 2πrdr* mass density p(r) M = ∫ 0 20 2 π r p ( r ) d r M = 2 π ∫ 0 20 r p ( r ) d r M = 2 π ∫ 0 20 r ( 0.03 + 0.01 cos ( π r 2 ) ) d r M = 2 π [ ∫ 0 20 0.03 r d r + ∫ 0 20 0.01 r cos ( π r 2 ) d r ] M = 2 π [ 0.03 ∫ 0 20 r d r + 0.01 ∫ 0 20 r cos ( π r 2 ) d r ] M = 2 π [ 0.03 [ r 2 2 ] 0 20 + 0.01 ∫ 0 20 r cos ( π r 2 ) d r ] M = 2 π [ 0...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6.2, Problem 32E

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To find: the total mass of circular plate of radius 20 cm whose mass density $p (r) = 0.03 + 0.01 \cos (π r^{2}) g / c m^{2}$

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Chapter 6.2, Problem 31E

Chapter 6.2, Problem 33E

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Chapter 6 Solutions

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the total mass of circular plate of radius 20 cm whose mass density p ( r ) = 0.03 + 0.01 cos ( π r 2 ) g / c m 2

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To find: the total mass of circular plate of radius 20 cm whose mass density p(r)=0.03+0.01cos(πr2)g/cm2

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Chapter 6 Solutions

To find: the total mass of circular plate of radius 20 cm whose mass density $p (r) = 0.03 + 0.01 \cos (π r^{2}) g / c m^{2}$