A circular disc of radius R is removed from a bigger circular disc of radius 2R, such that the circumferences of the disc coincide. The centre of mass of the new disc is αR from the centre of the bigger disc. The value of α is

For finding the value of α as in the extraction of a small disc from the larger disc we take the arrangement, we assume we have large disc with a radius of size 2R and small disc of radius R. After we take out small disc, now we want to know the location of new centre of mass due to this.

The larger disc has a larger area and mass, so it is initially centered at the origin. The smaller disc that is removed is also centered at the same point. The area and mass of the larger disc are proportionally greater than those of the smaller disc. This difference in mass distribution affects the position of the new center of mass after the smaller disc is removed.

As we analyze the situation, we can infer that the removal of the smaller disc will shift the center of mass toward the larger disc. Applying the principles of mass distribution and balance, we find that the center of mass of the remaining shape is located at a distance of αR from the center of the larger disc. After calculations, we conclude that the value of α is one-third which indicates the relative position of the center of mass in the modified structure.

See More:
https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/