A) \[\frac{1-e}{1+e}\]
B) \[\frac{1+e}{1-e}\]
C) \[\frac{e-1}{1-e}\]
D) \[\frac{e-1}{1+e}\]
Correct Answer: A
Solution :
\[e=\frac{{{v}_{2}}-{{v}_{1}}}{{{u}_{1}}-{{u}_{2}}}=\frac{{{v}_{2}}-{{v}_{1}}}{u-0}\] \[\Rightarrow \] \[{{v}_{2}}-{{v}_{1}}=e\,\,u\] By conservation of momentum, \[mu=m{{v}_{1}}+m{{v}_{2}}\] \[\Rightarrow \] \[{{v}_{1}}+{{v}_{2}}=u\] On solving,\[\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{1-e}{1+e}\]
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