A) \[\frac{1-e}{1+e}\]
B) \[\frac{e}{e+1}\]
C) 2/e
D) \[\frac{e+1}{2e}\]
Correct Answer: A
Solution :
Given, \[{{m}_{1}}={{m}_{2}}=m,{{u}_{1}}=u\]and \[{{u}_{2}}=0\] Let\[{{v}_{1}}\] and \[{{v}_{2}}\]be their velocities after collision. According to momentum conservation, \[mu=m({{v}_{1}}+{{v}_{2}})\] ?(i) or \[u={{v}_{1}}+{{v}_{2}}\] By definition\[e=\frac{{{v}_{2}}-{{v}_{1}}}{u-0}\] or \[{{v}_{2}}-{{v}_{1}}=eu\] ?(ii) Solving Eqs. (i) and (ii), we have \[{{v}_{1}}=\frac{(1-e)u}{2}\]and \[{{v}_{2}}=\left( \frac{1+e}{2} \right)u\] \[\Rightarrow \] \[\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{1-e}{1+e}\]
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