A) \[{{[(A-1)/(A+1)]}^{2}}\]
B) \[{{[(A+1)/(A-1)]}^{2}}\]
C) \[{{[(A-1)/A]}^{2}}\]
D) \[{{[(A+1)/A]}^{2}}\]
Correct Answer: A
Solution :
| \[\text{v}{{'}_{1}}=\frac{({{m}_{1}}-{{m}_{2}}){{\text{v}}_{\text{1}}}+2{{m}_{2}}{{\text{v}}_{2}}}{{{m}_{1}}+{{m}_{2}}}\] |
| As \[{{\text{v}}_{2}}\] is zero, \[{{m}_{2}}>{{m}_{1}},\] \[\text{v}{{'}_{1}}\]is in the opposite direction. |
| \[{{m}_{1}}=1,\,\,{{m}_{2}}=A.\] |
| \[\therefore \,\,\,|\text{v}{{\text{ }\!\!'\!\!\text{ }}_{\text{1}}}|\,\,=\,\,\frac{(A-1)}{(A+1)}{{\text{v}}_{1}}\] |
| The fraction of total energy retained is \[\frac{\text{1/2 mv}{{\text{ }\!\!'\!\!\text{ }}_{\text{1}}}^{\text{2}}}{\text{1/2 m}{{\text{v}}_{\text{1}}}^{\text{2}}}=\frac{{{(A-1)}^{2}}}{{{(A+1)}^{2}}}\] |
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