List of top Physics Questions on Centre of mass asked in EAMCET

A circular disc of radius $R$ is removed from a bigger circular disc of radius $2 R$ such that the circumferences of the discs touch. The centre of mass of the new disc is at a distance $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is

Three particles each of mass 1 kg are placed at the corners of a right angled triangle AOB, O being the origin of the coordinate system (OA and OB along positive X- direction and positive Y- direction). If OA=OB=1m, the positive vector of the centre of mass (in metres) is: