$A$ uniform disc of radius $R$ is placed over another uniform disc of radius $2R$ made of the same material and having the same thickness. The peripheries of the two discs touch each other. Locate the centre of mass of the system,taking the center of the large disc at the origin.

An isolated particle of mass $m$ is moving in a horizontal $x-y$ plane along the $x-$axis at a certain height above the ground. It suddenly explodes into two fragments of masses $m/4$ and $3m/4$. An instant later,the smaller fragment is at $y = 15 \ cm$. The larger fragment at this instant is at $y = \dots \ cm$.

$A$ 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

The figure shows two cylindrical rods whose centers of mass are marked as $A$ and $B$. The line $AB$ divides the region into two parts: one containing point $O$ (region $1$) and the other containing point $O'$ (region $2$). Choose the correct option regarding the center of mass of the combined system.

If the density of the material of a circular plate and a square plate as shown is the same,the center of mass of the composite system will be:

Which of the following statements regarding the centre of mass is $NOT$ true?