Three identical spheres,each of mass $1 \ kg$,are placed touching each other with their centres on a straight line. Their centres are marked $K, L$,and $M$ respectively. The distance of the centre of mass of the system from $K$ is

$A$ uniform square plate is shown in the figure. Four identical squares are removed from its corners. If squares $1$ and $3$ are removed,where will the center of mass $(C.M.)$ be located?

Particles of masses $m, 2m, 3m, \ldots, nm$ grams are placed on the same line at distances $l, 2l, 3l, \ldots, nl$ cm from a fixed point. The distance of the centre of mass of the particles from the fixed point in centimetres is:

Seven identical homogeneous bricks,each of length $L$,are arranged as shown in the figure. Each brick is displaced with respect to the one in contact by $\frac{L}{10}$. Calculate the $x$-coordinate of the centre of mass of this system relative to the origin $O$ as shown.

Centre of mass $(C.M.)$ of three particles of masses $1 \,kg, 2 \,kg$ and $3 \,kg$ lies at the point $(1, 2, 3)$ and $C.M.$ of another system of particles of $3 \,kg$ and $2 \,kg$ lies at the point $(-1, 3, -2)$. Where should we put a particle of mass $5 \,kg$ so that the $C.M.$ of the entire system lies at the $C.M.$ of the first system?

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.