Four identical particles each of mass $m$ are kept at the four corners of a square of side $a$. If one of the particles is removed,the shift in the position of the centre of mass is

Obtain the general expression for the centre of mass of a system of $n$ distributed particles in three dimensions.

$A$ solid cylinder of mass $2 \ kg$,length $40 \ cm$ and radius $10 \ cm$ is placed in contact with a solid sphere of mass $0.5 \ kg$ and radius $10 \ cm$ such that the centres of the two bodies lie along the geometrical axis of the cylinder. The distance of the centre of mass of the system of two bodies from the centre of the sphere is (in $cm$)

$A$ uniform disc of radius $R$ is placed over another uniform disc of radius $2R$ made of the same material and having the same thickness. The peripheries of the two discs touch each other. Locate the centre of mass of the system,taking the center of the large disc at the origin.

Two objects $A$ and $B$ of masses $M$ and $m$ respectively,where $M > m$,are separated by a distance. They move towards each other under the influence of equal forces. At what point will they collide?

$A$ uniform square plate $abcd$ has a mass of $1 \, kg$. If two point masses,each of $20 \, g$,are placed at the corners $b$ and $c$ as shown,then the centre of mass shifts on the line