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, \[mu=m({{v}_{1}}+{{v}_{2}})\] or \[u={{v}_{1}}+{{v}_{2}}\] ... (i) 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 \[{{v}_{2}}=\left( \frac{1+e}{2} \right)u\] \[\Rightarrow \] \[\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{1-e}{1+e}\]You need to login to perform this action.
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