Question

The position of the centre of mass of a system consisting of two particles of masses $m_1$ and $m_2$, separated by distance $L$, from $m_2$ is

• A. $\left(\frac{m_{2}L}{m_1+m_2}\right)$
• B. $\left(\frac{m_1{m}_{2}L}{m_1^2+m_2^2}\right)$
• C. $\left(\frac{m_1}{m_2}L\right)$
• D. $\left(\frac{m_{1}L}{m_1+m_2}\right)$

Answer 1

The correct option is D $\left(\frac{m_{1}L}{m_1+m_2}\right)$


Here position of $m_1$ is taken as reference i.e $r_1=0$
$r_2$ = position of $m_2$ from $m_1=L$
Position of centre of mass of two discrete particles :
$r_{COM}=\frac{m_1{r}_1+m_2{r}_2}{m_1+m_2}=\frac{m_2\ast L}{m_1+m_2}$
Distance of COM from $m_1$
$=L-\left(\frac{m_{2}L}{m_1+m_2}\right)=\frac{m_{1}L}{m_1+m_2}$ from $m_2$