Answer
$\frac{2L}{3}$
Work Step by Step
We know:
$\frac{dm}{M} = \frac{2xdx}{L^2}$
We obtain the following integral from this:
$x_{cm} = \frac{1}{M} \int xdm = \frac{2}{L^2} \int_0^Lx^2dx =\frac{2L}{3} $
Essential University Physics: Volume 1 (4th Edition)
by Wolfson, Richard
Published by
Pearson
ISBN 10:
0-134-98855-8
ISBN 13:
978-0-13498-855-9
Chapter 9 - Section 9.1 - Center of Mass - Example - Page 153: 9.3
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