The centre of mass of a system of two particles of masses $m_1$ and $m_2$ separated by a distance $d$ is:

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.

Four masses are arranged along a circle of radius $1 \ m$ as shown in the figure. The center of mass of this system of masses is at

$A$ point mass $m_A$ is connected to a point mass $m_B$ by a massless rod of length $l$ as shown in the figure. It is observed that the ratio of the moment of inertia of the system about the two axes $AA$ and $BB$,which are parallel to each other and perpendicular to the rod,is $\frac{I_{BB}}{I_{AA}} = 3$. The distance of the centre of mass of the system from the mass $m_A$ is

$A$ particle of mass $m$ is moving in the $xy$-plane at a certain height from the ground along the $x$-axis. It suddenly explodes into two fragments of masses $m/4$ and $3m/4$. At that instant,the smaller fragment is at $y = 15 \ cm$. At this instant,the larger fragment will be at $y = $ ........ $cm$.

Three circular discs of same material and same thickness of radii $r, 2r$ and $3r$ are placed on a horizontal plane such that their centres lie along a straight line. The radius of the middle disc is $2r$ and it touches the other two discs. The distance of the centre of mass of the system from the centre of the smaller disc is . . . . . . . (in $r$)