A) \[\frac{1+e}{1-e}\]
B) \[\frac{1-e}{1+e}\]
C) \[\frac{e}{1-e}\]
D) \[\frac{1+e}{e}\]
Correct Answer: B
Solution :
Let \[{{v}_{1}},{{v}_{2}}\]be the final velocities of the two spheres. Applying the law of conservation of linear momentum \[mu=m({{v}_{1}}+{{v}_{2}})\] or \[{{v}_{1}}+{{v}_{2}}=u\] ?(i) Again the coefficient of restitution is given by \[e=\frac{{{v}_{2}}-{{v}_{1}}}{u}\] or \[{{v}_{2}}-{{v}_{1}}=eu\] ?(ii) Solving Eqs. (i) and (ii), we get \[{{v}_{1}}=\frac{u}{2}(1-e),{{v}_{2}}=\frac{u}{2}(1+e)\] Therefore, \[\frac{{{v}_{1}}}{{{v}_{2}}}=\left( \frac{1-e}{1+e} \right)\]
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