question_answer

Consider a system of two particles having masses \[{{m}_{1}}\]and \[{{m}_{2}}\]. If the particle of mass \[{{m}_{1}}\] is pushed towards the mass centre of particles through a distance 'd?, by what distance would the particle of mass \[{{m}_{2}}\] move so as to keep the mass centre of particles at the original postion:-

A)  \[\frac{{{m}_{1}}}{{{m}_{2}}}\,d\]            

B)  \[d\]

C)  \[\frac{{{m}_{2}}}{{{m}_{1}}}\]                                

D)  \[\frac{{{m}_{1}}}{{{m}_{1}}+{{m}_{2}}}\,d\]

Correct Answer: A

Solution :

\[{{m}_{1}}{{r}_{1}}={{m}_{2}}{{r}_{2}}\]                          ???(1) \[{{m}_{1}}({{r}_{1}}-d)={{m}_{2}}({{r}_{2}}-d')\]      ??? (2) from (1) and (2) we get \[d'=\frac{{{m}_{1}}}{{{m}_{2}}}\,d\]