2. Let r > 0, and let R be the semicircular region bounded below by the x axis and above by the circle x2 + y? = r2, that is, x² + y? = r2 with y > 0. (a) Find the center of gravity (7, g) of R. (b) Find the radius r for which (7, g) (0, T). (c) Suppose S is the quarter circular region in the first quadrant, bounded by the x axis, the axis, and the quarter circle x2 + y² = r². Without evaluating any integrals or making further computations, use symmetry considerations and computations in (a) to determine (T, 9).
2. Let r > 0, and let R be the semicircular region bounded below by the x axis and above by the circle x2 + y? = r2, that is, x² + y? = r2 with y > 0. (a) Find the center of gravity (7, g) of R. (b) Find the radius r for which (7, g) (0, T). (c) Suppose S is the quarter circular region in the first quadrant, bounded by the x axis, the axis, and the quarter circle x2 + y² = r². Without evaluating any integrals or making further computations, use symmetry considerations and computations in (a) to determine (T, 9).
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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Transcribed Image Text:2. Let r> 0, and let R be the semicircular region bounded below by the x axis and above by the circle
x² + y? = r², that is, x? + y? = p2 with y > 0.
(a) Find the center of gravity (x, F) of R.
(b) Find the radius r for which (7, g) = (0, T).
(c) Suppose S is the quarter circular region in the first quadrant, bounded by the x axis, the y
axis, and the quarter circle x? + y² = r2. Without evaluating any integrals or making further
computations, use symmetry considerations and computations in (a) to determine (7, g).
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Let r > 0, and let R be the semicircular region bounded below by the x axis and above by the circle ,
That is, with .
(a) The region R is show here,
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