Two particles of mass $5\, kg$ and $10\, kg$ respectively are attached to the two ends of a rigid rod of length $1\, m$ with negligible mass. The centre of mass of the system from the $5\, kg$ particle is nearly at a distance of $..........\, cm$.

$A$ 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.

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.

$A$ thin uniform wire is bent to form the two equal sides $AB$ and $AC$ of triangle $ABC$,where $AB = AC = 5\,cm$. The third side $BC$,of length $6\,cm$,is made from a uniform wire of twice the linear density of the first. The distance of the centre of mass from $A$ is

The centre of mass of three particles of masses $1 \ kg, 2 \ kg$ and $3 \ kg$ is at $(2, 2, 2)$. The position of the fourth mass of $4 \ kg$ to be placed in the system so that the new centre of mass is at $(0, 0, 0)$ is:

$A$ rod of length $3\, m$ has a mass per unit length directly proportional to the distance $x$ from one of its ends. The center of gravity of the rod from that end will be at ........ $m$.