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This problem uses cylindrical coordinates z, r, 0 with r² = x² + y°. Let H, m > 0. Consider a solid cone G defined by z < H and z > mr, where m = cot(4.) and the angle between the lateral surface of the cone and the central axis of the cone is ,. See Figure 1. 2mr FIGURE 1. A cone of height H and central angle o,. Find the centroid (2, 9, 2) of G. Note that the cone becomes very narrow as o, → 0*, or equivalently, as m + +oo. Take your answer for the centroid above and compute the limit lim (7, §, 2). Finally does vour answer surprise vou?

This problem uses cylindrical coordinates z, r, 0 with r² = x² + y°. Let H, m > 0. Consider a solid cone G defined by z < H and z > mr, where m = cot(4.) and the angle between the lateral surface of the cone and the central axis of the cone is ,. See Figure 1. 2mr FIGURE 1. A cone of height H and central angle o,. Find the centroid (2, 9, 2) of G. Note that the cone becomes very narrow as o, → 0*, or equivalently, as m + +oo. Take your answer for the centroid above and compute the limit lim (7, §, 2). Finally does vour answer surprise vou?

Advanced Engineering Mathematics
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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This problem uses cylindrical coordinates 2,r, 0 with r? = r² + y?. Let H, m > 0. Consider a solid cone G defined by z < H and z > mr, where m = cot(4.) and the angle between the lateral surface of the cone and the central axis of the cone is o.. See Figure 1. %3D 2= H 2=mr FIGURE 1. A cone of height H and central angle o.. Find the centroid (7, ỹ, z) of G. Note that the cone becomes very narrow as o, → 0*, or equivalently, as m → +o. Take your answer for the centroid above and compute the limit lim (7, ỹ, 2). Finally, does your answer surprise you?
Transcribed Image Text:This problem uses cylindrical coordinates 2,r, 0 with r? = r² + y?. Let H, m > 0. Consider a solid cone G defined by z < H and z > mr, where m = cot(4.) and the angle between the lateral surface of the cone and the central axis of the cone is o.. See Figure 1. %3D 2= H 2=mr FIGURE 1. A cone of height H and central angle o.. Find the centroid (7, ỹ, z) of G. Note that the cone becomes very narrow as o, → 0*, or equivalently, as m → +o. Take your answer for the centroid above and compute the limit lim (7, ỹ, 2). Finally, does your answer surprise you?
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