Question

Two particles of masses $1\text{kg}$ and $2\text{kg}$ are located at $x=0$ and $x=3\text{m}$. The position of their centre of mass is given by the co-ordinates

• A. $(1,0)$
• B. $(2,0)$
• C. $(0,2)$
• D. $(\frac{3}{2},0)$

Answer 1

The correct option is B $(2,0)$

Since, both the particles lie on $x-$axis, the COM will also lie on $x-$axis.

Let the COM is located at $x=x$, then

$r_1=$ distance of COM from the particle of mass $1\text{kg}=x$,

$r_2=$ distance of COM from the particle of mass $2\text{kg}=(3-x)$

Using the relation, $\frac{r_1}{r_2}=\frac{m_2}{m_1}$

$\frac{x}{3-x}=\frac{2}{1}$

$\therefore x=2\text{m}$

Thus, the COM of the two particles is located at $x=2\text{m}$.

Therefore, option $\left(B\right)$ is correct.

Alternate solution:

The $x$ - coordinate of $\text{COM}$ is given by,

$x_{COM}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}$

$x_{COM}=\frac{1\left(0\right)+2\left(3\right)}{1+2}=2\text{m}$

Why this question: This question requires the basic application of the formula of position of COM.