Three masses are placed on the $x-$axis: $300 \, g$ at the origin,$500 \, g$ at $x = 40 \, cm$ and $400 \, g$ at $x = 70 \, cm$. The distance of the centre of mass from the origin is ....... $cm$.

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

$A$ 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:

$A$ 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

$A$ particle of mass $m$ is moving in the $xy$-plane at a certain height from the ground along the $x$-axis. It suddenly explodes into two fragments of masses $m/4$ and $3m/4$. At that instant,the smaller fragment is at $y = 15 \ cm$. At this instant,the larger fragment will be at $y = $ ........ $cm$.

When two masses $m$ and $M$ $(M > m)$ are connected,where will the center of mass be located?