Question

If two masses of $2kg$ and $6kg$ are located at certain distance. If $6kg$ mass is moved 3cm rightward. Find the location of $2kg$ mass.

Answer 1

In the absence of any external force there COM will remains stationary
$\Delta X_{com}=0=\frac{m_1{\Delta }_1+m_2\Delta x_2}{m_1+m_2}$
$m_1\Delta x_1=-m_2\Delta x_2$
$2\times \Delta x_1=6\times 3cm$
$\Delta x_1=-9cm$
$2kg$ mass will move 9cm leftward.