Question

There are two masses $m_1$ and $m_2$ placed at a distance l apart. Let the centre of mass of this system is at a point named C. If $m_1$ is displaced by $l_1$, towards C and $m_2$ is displaced by $l_2$ away from C. Find the distance, from C where new centre of mass will be located.

Answer 1

From given, we have,

$m_{1}x=m_2(L-x)$

$\Rightarrow x=\frac{m_{2}L}{m_1+m_2}$..........(1)

$m_1$ displaced by $L_1$ and $m_2$ displaced by $L_2$, with new centre of mass $C$

we have,

$m_1(L_1+x-y)=m_2(L-x+y+L_2)$........(2)

from (1) and (2), we have,

$m_1(L_1+\left(\frac{m_{2}L}{m_1+m_2}\right)-y)=m_2(L-\left(\frac{m_{2}L}{m_1+m_2}\right)+y+L_2)$

upon simplification, we get the value of "y" as,

$y=\frac{m_1{L}_1-m_{2}L}{m_1+m_2}$