Consider a system of two particles having masses $m_{1}$ and $m_{2}$. If the particle of mass $m_{1}

Question

Consider a system of two particles having masses $m_{1}$ and $m_{2}$. If the particle of mass $m_{1}$ is pushed towards the centre of mass of the particles through a distance $d$, by what distance would be particle of mass $m_{2}$ move so as to keep the centre of mass of the particles at the original position?\

Professor PC Thomas Classes · Answer

(b) : C.M. $=\frac{m_{1} x_{1}+m_{2} x_{2}}{m_{1}+m_{2}}$ After changing position of $m_{1}$ and to keep the position of C.M. same\ C.M. $=\frac{m_{1}\left(x_{1}-dight)+m_{2}\left(x_{2}+d_{2}ight)}{m_{1}+m_{2}}$ $$ 0=\frac{-m_{1} d+m_{2} d_{2}}{m_{1}+m_{2}} \quad[	ext { Substituting value of C.M. from (i) }] $$ $$ \Rightarrow \quad d_{2}=\frac{m_{1}}{m_{2}} d $$