Explanation Given: p ( r ) = 4 r g / c m 2 Calculation: We have been given that, radius of circular plate = 2 cm and mass density = p ( r ) = 4 r 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 2 2 π r p ( r ) d r M = 2 π ∫ 0 2 r p ( r ) d r M = 2 π

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 6.2, Problem 34E

To determine

To show: that a circular plate of radius 2 cm with radial mass density $p (r) = \frac{4}{r} g / c m^{2}$ has finite total mass, even though the density becomes infinite at the origin.

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Chapter 6.2, Problem 33E

Chapter 6.2, Problem 35E

Chapter 6 Solutions

CALCULUS (CLOTH)

Ch. 6.1 - Prob. 1PQ Ch. 6.1 - Prob. 2PQ Ch. 6.1 - Prob. 3PQ Ch. 6.1 - Prob. 4PQ Ch. 6.1 - Prob. 5PQ Ch. 6.1 - Prob. 6PQ Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E

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that a circular plate of radius 2 cm with radial mass density p ( r ) = 4 r g / c m 2 has finite total mass, even though the density becomes infinite at the origin.

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To show: that a circular plate of radius 2 cm with radial mass density p(r)=4rg/cm2 has finite total mass, even though the density becomes infinite at the origin.

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Chapter 6 Solutions

To show: that a circular plate of radius 2 cm with radial mass density $p (r) = \frac{4}{r} g / c m^{2}$ has finite total mass, even though the density becomes infinite at the origin.