?Consider the solid enclosed by the cylinder \(x^{2}+z^{2}=a^{2}\) and the planes y = b

Chapter 5, Problem 353

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Consider the solid enclosed by the cylinder \(x^{2}+z^{2}=a^{2}\) and the planes y = b and y = c, where a > 0 and b < c are real numbers. The density of Q is given by \(\rho(x, y, z)=f^{\prime}(y)\), where f is a differential function whose derivative is continuous on (b, c). Show that if f(b) = f(c), then the moment of inertia about the xz-plane of Q is null.

Text Transcription:

x^2 + z^2 = a^2

rho(x, y, z) = f^prime (y)

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