(Solution) - The assumption of uniform mass density in Problem 44 is -(2025 Original AI-Free Solution)

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The assumption of uniform mass density in Problem 44 is rather unrealistic. For most galaxies, the mass density increases greatly toward the center of the galaxy. Repeat Problem 44 using a surface mass density of the form s(r) = C/r, where s(r) is the mass per unit area of the disk at a distance r from the center. First determine the constant C in terms of R and M; then proceed as in Problem 44.