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 $r$)

Write a short note on the centre of gravity.

Two uniform plates of the same thickness and area but of different materials,one shaped like an isosceles triangle and the other shaped like a rectangle,are joined together to form a composite body as shown in the figure. If the centre of mass of the composite body is located at the mid-point of their common side,then the ratio between the masses of the triangle to that of the rectangle is:

Where is the centre of mass of two isolated particles of equal mass located?

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.

$A$ 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: