# Chapter 9 - Exercises and Problems - Page 163: 17

$(0, \frac{L \sqrt3}{6})$

#### Work Step by Step

We construct a coordinate system where the origin is located at the center of the base of the triangle. Finding the x center of mass is simple: since the object is symmetric, we can conclude that the center of mass must be at x=0. Next, we must find the y center of mass. $y_{cm} = \frac{my_1+my_2+my_3}{m+m+m}$ $y_{cm} = \frac{m(0)+m(0)+m \frac{L \sqrt3}{2}}{m+m+m}$ $y_{cm}=\frac{L \sqrt3}{6}$

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