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 December 1st, 2011, 11:15 AM #1 Member   Joined: Sep 2010 Posts: 39 Thanks: 0 center mass The region between, y=1/x and the x axis from x=1 to x=7 is revolved about the x axis. find the CM of thin plate covering the region if the plates density at (x,y) is sqrt x Trying to understand the formula to solve. thanks.
 December 1st, 2011, 12:14 PM #2 Senior Member   Joined: Nov 2011 Posts: 595 Thanks: 16 Re: center mass The center of mass is on the x axis by symmetry. So you have to: 1) Calculate the total mass which is $M=\int \rho dV=\int_{1}^{7}\rho\pi y^2(x)dx=\int_{1}^{7}\frac{\rho\pi}{x^2}dx$ (because $\pi y^2(x)$ is the area of the circle at abscissa x) 2) Then the abcisse $x_G$ of the center of mass is $x_G=(1/M)\int_{1}^{7}\frac{x\rho\pi}{x^2}dx$ PS: I wrote that quickly so check twice that there is no mistake or typos but the spirit should be there! Good luck.

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