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\noindent {\bf Problem statement} A thin plate (lamina) of uniform
density $\rho$ covers the portion of the $xy$ plane lying in the first
quadrant and between two circles centered at the origin. The inner
circle has radius $a$ and the outer, $b$. The coordinates of points
covered by this plate satisfy $x,y\ge0$ and $a^2\le x^2+y^2\le b^2$ as
shown.

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\noindent a) Find the coordinates $(\bar x,\bar y)$ of the center of
mass $P$ of this plate.  (How can symmetry simplify this problem?)
 
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\noindent b) Suppose now that $b=1$.  From your answer in a) determine
for what values of $a$ the center of mass $P$ lies inside the area
covered by the plate (as shown in the figure).

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