Three identical spheres, each of mass $m$ kg, are kept touching each other, with their centers on a straight line. If their centers are marked as $A$, $B$, and $C$ respectively, the distance of the center of mass of the system from $A$ is

On what does the position of the center of mass of a rigid body depend?

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:

Each side of a rhombus has length $a$. Four particles of masses $m, 2m, 3m$ and $4m$ are placed at the vertices of the rhombus. The angle between two adjacent sides of the rhombus is $60^o$. The rhombus lies in the $x-y$ plane,with mass $m$ at the origin and mass $4m$ on the $x$-axis. Find the coordinates of the center of mass of this system.

The distance of the centre of mass from end $A$ of a one-dimensional rod $(AB)$ having mass density $\rho = \rho_{0} \left(1 - \frac{x^{2}}{L^{2}}\right) \text{ kg/m}$ and length $L$ (in meters) is $\frac{3L}{\alpha} \text{ m}$. The value of $\alpha$ is $\ldots \ldots \ldots$ (where $x$ is the distance from end $A$).

Five masses are placed in a plane as shown in the figure. The coordinates of the centre of mass are nearest to: