Look up the position of the centre of mass C of a semi-circularOriginally Posted by brandon26
lamina. Assume the lamina's radius is 1 (doesn't matter what it actually
is as we are after a ratio, but if it worries you call it r). This will
be on the line AB.
The centre of mass of your lamina+particle is at the same position
as the centre of mass of two particles one of mass M at C, and one
of mass m at B.