Question

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

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

Answer 1

Answer: (B)

$(2,2)$

Let masses are kept at points A, B and C where $P$ denotes the centre of mass of the system which lies at a distance $x$ from point A.

Using $x=\frac{m_1{r}_1+m_2{r}_2+m_3{r}_3}{m_1+m_2+m_3}$

$\therefore$ $x=\frac{m\times 0+m\times 1+m\times 2}{m+m+m}=\frac{3m}{3m}=1$

Thus the centre 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 centre of mass of the system lies at $(2,2)$