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 centre of mass of the system from $K$ is
$\frac{{KL + KM + LM}}{3}$
$\frac{{KL + KM}}{3}$
$\frac{{KL + LM}}{3}$
$\frac{{KM + LM}}{3}$
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 uniform wire of twice the density of the first. The distance of centre of mass from $A$ is
Mention the centre of mass of three particles which are not in line but have equal masses.
Mass is distributed uniformly over a thin square plate. If two end points of diagonal are $(-2, 0)$ and $(2, 2)$, what are the coordinates of centre of mass of plate ?
Find the centre of mass of a uniform L-shaped lamina (a thin flat plate) with dimensions as shown. The mass of the lamina is $3 \;kg$.
$(n - 1)$ equal point masses each of mass $m$ are placed at the vertices of a regular $n-$ polygon. The vacant vertex has a position vector $a$ with respect to the centre of the polygon. Find the position vector of centre of mass.