The centre of mass of a homogeneous semi-circular plate of radius $r$ is located at $A$ as shown in the figure. The distance $OA$ is

The distance between the carbon atom and the oxygen atom in a carbon monoxide molecule is $1.1 \ \mathring{A}$. Given,mass of carbon atom is $12 \ a.m.u.$ and mass of oxygen atom is $16 \ a.m.u.$,calculate the position of the center of mass of the carbon monoxide molecule.

Four masses $1 \ kg, 1 \ kg, 2 \ kg$ and $2 \ kg$ are placed at the four corners $P, Q, R$ and $S$ of a square of side $a$ respectively. The center of mass of the system will be farthest from which of the following?

The centre of mass of two thin uniform rods of the same length $L$ but made of different materials and kept as shown in the figure can be,if the meeting point is the origin of coordinates:

Two particles of masses $m_1$ and $m_2$ are separated by a distance $d$. The shift in the centre of mass when the two particles are interchanged is:

Four particles of masses $m, 2m, 3m$ and $4m$ are arranged at the corners of a parallelogram with each side equal to $a$ and one of the angles between two adjacent sides is $60^o$. The parallelogram lies in the $x-y$ plane with mass $m$ at the origin and $4m$ on the $x$-axis. The centre of mass of the arrangement will be located at