Problem $5(15$ points$)$ Figure shows a uniform metal plate of radius $2R$ from which

a disk of radius $R$ has been stamped out $($removed$).$

a$)$ Using the $x-y$ coordinate system shown, locate the center of mass

of the plate.

b$)$ Now the removed disk is welded to the plate as shown

in the figure. Find the center of mass of the combined

system.