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:

$A$ uniform rod of length $L$ and mass $M$ is placed along the $x$-axis with its one end at the origin. The centre of mass of the rod is located at:

The balls $A, B$ and $C$ of masses $50 \ g, 100 \ g$ and $150 \ g$,respectively,are placed at the vertices of an equilateral triangle. The length of each side is $1 \ m$. If $A$ is placed at $(0,0)$ and $B$ is placed at $(1,0) \ m$,find the coordinates $(x, y)$ for the centre of mass of this system of the balls.

Which of the points is the likely position of the centre of mass of the system shown in the figure?

Find the center of mass $(x, y, z)$ of the following structure of four identical cubes if the length of each side of a cube is $1$ unit.

$A$ $T$-shaped object is placed on a smooth surface as shown in the figure. $A$ force $\vec{F}$ is applied at point $P$ in a direction parallel to $AB$ such that the object undergoes pure translational motion without rotation. Find the position of point $P$ relative to point $C$.