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 \[d'=\frac{{{m}_{1}}}{{{m}_{2}}}\,d\]