Question

Two particles of masses $m_1$ and $m_2$ are located at $x=0\text{m}$ and $x=6\text{m}$. If the position of their centre of mass is at $x=4\text{m}$, then the ratio of their masses $\frac{m_2}{m_1}$ is

• A. $2$
• B. $1$
• C. $4$
• D. $3$

Answer 1

The correct option is A $2$

As we know, the distance of centre of mass from any particle $\left(x\right)$ is inversely proportional to the mass of particle $\left(m\right)$
$x_1$ is distance of $m_1$ from $COM$ = $4\text{m}$
$x_2$ is distance of $m_2$ from $COM$ = $2\text{m}$
$x\propto \frac{1}{m}\Rightarrow \frac{x_1}{x_2}=\frac{m_2}{m_1}$
$\Rightarrow \frac{4}{2}=\frac{m_2}{m_1}$
or $\frac{m_2}{m_1}=2$