Question

From a uniform disc of radius R,an equilateral triangle of side root3R is cut . the new position of centre of mass???

Answer 1

The length of side √3 R of the equilateral triangle cut out from the disc means it is the largest equilateral triangle that can be possible on the disc of radius R.

It is symmetric about the center of the circle.  The centroid of the triangle coincides with the center of the circle. The vertices of the triangle are on the circumference. The circle is the circumcircle.

So after the triangle is cut out, the remaining mass is symmetric about the center. Hence the center of mass remains at the same position.