The centre of mass of two thin uniform rods of the same length $L$ but made of different materials and kept as shown in the figure can be,if the meeting point is the origin of coordinates:

Define the position vector of the centre of mass.

Masses $m \left(\frac{1}{3}\right)^N \frac{1}{N}$ are placed at $x=N$,where $N=2, 3, 4, \ldots \infty$. If the total mass of the system is $M$,then the centre of mass is

$A$ uniform thin rod of length $L$ and mass $M$ is placed along the $x$-axis with one end at the origin. Find the position of the centre of mass of the rod.

The linear mass density of a rod of length $L$ varies as $\lambda = A + Bx$. Find the center of mass.

The centre of mass of a non-uniform rod of length $L$ whose mass per unit length $\lambda$ varies as $\lambda = \frac{k x^3}{L^3}$ (where $k$ is a constant and $x$ is the distance of any point on the rod from one end) is at a distance from the same end equal to: