An object in the shape square with a circle cut in the center of it spins about

Question

An object in the shape square with a circle cut in the center of it spins about it ceter of mass. The axis of rotation is perpendicualr to the plane of the square. The object has mass M and has edges of lenght 2R. Its density is constant

1) Let M(s) be the mass of whole square and M(c) be the mass of the circle that was cut out of the square to make the object. Express the moment of Inertia of this object in terms of M(s), M(c) and R

2) how does the objects mass M relate to the masses of M(s), M(c)

3) What is the ratio of M(s) and M(c)

4) what is moment of inertia in terms of M and R

5) use 2 and 3 to express M(s) and M(c) totally in terms of M

Thanks

Explanation / Answer

whenever there is any such problem of MOI of any cut off portion, the problem needs to be solved in this manner only where the mass that is cut off, is taken to be negative!!

thank you

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