Question

A system consists of three particles, each of mass $m$ and located at $(1,1),(2,2)$ and $(3,3)$. The co-ordinates of the center of mass are :

• A. (1, 1)
• B. (2,2)
• C. (3,3)
• D. (6,6)

Answer 1

Answer: (B)

(2,2)

Answer 2

Let masses are kept at points $A, B$ and $C$ where $P$ denotes the center of mass of the system which lies at a distance $x$ from point $A$.
Using $x=\frac{m_{1} r_{1}+m_{2} r_{2}+m_{3} r_{3}}{m_{1}+m_{2}+m_{3}}$
$\therefore x =\frac{ m \times 0+ m \times 1+ m \times 2}{ m + m + m }$
$=\frac{3 m }{3 m }=1$
Thus the center of mass of the system lies at distance of $1$ unit away from point $A$ om the line joining the masses i.e line $ABC$
Hence the center of mass of the system lies at $(2,2)$