Question

Two point particles of masses $1\text{kg}$ and $2\text{kg}$ are placed on an axis as shown in figure. The position of COM of the system would be

• A. $4\text{m}$ from $1\text{kg}$ mass
• B. $4\text{m}$ from $2\text{kg}$ mass
• C. At the midpoint between the two masses
• D. Close to $2\text{kg}$, but data insufficient

Answer 1

The correct option is A $4\text{m}$ from $1\text{kg}$ mass

Given, masses of particles $m_1=1\text{kg},m_2=2\text{kg}$
Taking $m_1\left(1\text{kg}\right)$ to be origin
Position of $1\text{kg}$ $(x_1,y_1)=(0,0)$
Position of $2\text{kg}$ $(x_2,y_2)=(6,0)$
Position of $COM$:
$x_{cm}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}=\frac{1\left(0\right)+2\left(6\right)}{3}$
$=4\text{m}$ from $m_1$