Q1: 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

ANS:C -

In brief, as the area is chopped off and the centroid is the sum( incremental area * distance to axis of centroid)/(total area).

Both numerator and denominator should have "minus" between them.

You can prove it mathematically finding the length of the square in terms of r.