Center of Mass of an L-shaped object!?
We have a square with side $A$ and we remove from one of its corners a square with side $B\lt A$. Questions: 1) What is the center of mass of this object? 2)What is the ratio of B/A such that the center of mass is inside the object? (we need to use the formula with the integrals $$Ycm = \frac{\int ydm}{\int dm}$$ and $$Xcm = \frac{\int xdm}{\int dm}$$) It was a question in a test I had recently at the university and it puzzled many people, myself included and I want to know the solution to it. Thank you for your help!
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$\begingroup$I don't think the large square has had a small square removed from it. I think it has had a small negative-mass square added to it, and that there are now two squares. So the question is about the combined centre of mass of two nice symmetrical objects, one of which has negative mass.
Being inside the L shape means being inside the large square and outside the small one.
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