Centre of mass of discrete massesEdexcel International A Level Further Maths: Mind map

Exam questions on Centre of mass of discrete masses

1. Particles of mass $2$ kg, $3$ kg and $5$ kg are placed on a straight horizontal line at distances $1$ m, $4$ m and $7$ m respectively from a fixed point $O$, all on the same side of $O$.
   Instead, a fourth particle of mass $10$ kg is placed at a distance $d$ m from $O$ so that the centre of mass of the four particles is $6$ m from $O$. Find $d$.2 marks
2. Particles of mass $2$ kg, $3$ kg and $5$ kg are placed at the points $(1,4)$, $(4,0)$ and $(3,2)$ respectively, where the coordinates are in metres relative to an origin $O$.
   Find the distance of the centre of mass from the origin $O$.2 marks
3. A light rod $AB$ has length $4$ m. Particles of mass $3$ kg, $m$ kg and $5$ kg are attached to the rod at $A$, at the midpoint of $AB$ and at $B$ respectively. The centre of mass of these three particles is $2.4$ m from $A$.
   Find the value of $m$.3 marks