Applied Mechanics and Graphic Statics
A square hole is punched out of a circular lamina, the diagonal of the square being the radius of the circle. If ‘r’ is the radius of the circle, the C.G. of the remainder from the corner of the square on the circumference will be

[r (π + 0.25)]/(π - 0.5)
[r (π - 0.25)]/(π - 0.5)
[r (π + 0.25)]/(π + 0.5)
[r (π - 0.5)]/(π + 0.25)

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Applied Mechanics and Graphic Statics
If a set of given forces are such that their free vectors build a closed polygon, then

The resultant force and resultant couple are always zero
The resultant force is zero but resultant couple is not zero
The resultant force and resultant couple both may not be zero
The resultant force is zero but resultant couple may not be zero

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