physics
posted by marwan .
Consider a square ABCD of side 10cm and total mass 10kg. Let O be the center of the sqaure. We cut a square of corners O and C.
Find the central mass of the obtained shape after removing the small cutten sqaure.

How big is the cutoff piece? You would need to that it most cases. (Not this time, however)
I think they want the Center of Mass, not the "Central Mass"  whatever that is.
You also probably meant "off corners A and C" instead of "of corners O and C". There IS no corner at O. Please be more precise with your problem copying.
In this case, because of the symmetry of removing opposite corners A and C, the center of mass will not move. 
Lets do it the math way.
cmenw*massnew=cmold*oldmasscmsquare*masssquare
now, doing it in each coordinate.
xcmnew*7.5=5*107.5*(10/4)=5018.75=31.25
xcmnew=4.166
ycmnew*7.5=5*102.5*10/4
=506.25=43.75
ycmnew=5.833
check all that.
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