A) \[\frac{{{m}_{1}}}{{{m}_{2}}}\]
B) \[\sqrt{\frac{{{m}_{1}}}{{{m}_{2}}}}\]
C) \[\frac{{{m}_{2}}}{{{m}_{1}}}\]
D) \[\sqrt{\frac{{{m}_{2}}}{{{m}_{1}}}}\]
Correct Answer: C
Solution :
[c] From linear momentum conservation, \[{{m}_{1}}{{v}_{1}}={{m}_{2}}{{v}_{2}}\]. As they move spring exerts equal and opposite forces on \[{{m}_{1}}\] and \[{{m}_{2}}\]. \[\Rightarrow \] \[{{m}_{1}}\frac{d{{x}_{1}}}{dt}={{m}_{2}}\frac{d{{x}_{2}}}{dt}\] \[\Rightarrow \] \[{{m}_{1}}\int{\,d{{x}_{1}}={{m}_{2}}\int{\,d{{x}_{2}}}}\] \[\Rightarrow \] \[{{m}_{1}}{{x}_{1}}={{m}_{2}}{{x}_{2}}\] \[\Rightarrow \] \[\frac{{{x}_{1}}}{{{x}_{2}}}=\frac{{{m}_{2}}}{{{m}_{1}}}\]You need to login to perform this action.
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