The centre of mass of two particles lies:

$A$ rod of length $3\, m$ has a mass per unit length directly proportional to the distance $x$ from one of its ends. The center of gravity of the rod from that end will be at ........ $m$.

The centre of mass of an extended body on the surface of the earth and its centre of gravity:

Look at the figure drawn with ink of uniform linear density. $A$ mass $m$ of ink is used to draw each of the two inner circles and each of the two line segments. $A$ mass $6m$ of ink is used to draw the outer circle. The coordinates of the centers of the different parts are: outer circle $(0, 0)$,left inner circle $(-a, a)$,right inner circle $(a, a)$,and the horizontal line segment $(0, -a)$. Find the $y$-coordinate of the center of mass of the ink in the figure.

Four bodies of masses $2\,kg, 3\,kg, 5\,kg$ and $8\,kg$ are placed at the four corners of a square of side $2\,m$ as shown in the figure. The position of the centre of mass $(CM)$ is:

Two objects of mass $10\,kg$ and $20\,kg$ respectively are connected to the two ends of a rigid rod of length $10\,m$ with negligible mass. The distance of the center of mass of the system from the $10\,kg$ mass is: