A) 0, 1
B) 1, 1
C) 1, 0.5
D) 0, 2
Correct Answer: A
Solution :
If two bodies collide head on with coefficient of restitution \[e=\frac{{{v}_{2}}-{{v}_{1}}}{{{u}_{1}}-{{u}_{2}}}\] ?(i) From the law of conservation of linear momentum\[{{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}={{m}_{1}}{{v}_{1}}+{{m}_{2}}{{v}_{2}}\] \[\Rightarrow \] \[{{v}_{1}}=\left[ \frac{{{m}_{1}}-e{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right]{{u}_{1}}+\left[ \frac{(1+e){{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right]{{u}_{2}}\] Substituting \[{{u}_{1}}=2\,m{{s}^{-1}},{{u}_{2}}=0,{{m}_{1}}=m\] and \[{{m}_{2}}=2m,e=0.5\]we get\[{{v}_{1}}=\left[ \frac{m-m}{m+2m} \right]\times 2\] \[\Rightarrow \] \[{{v}_{1}}=0\] Similarly, \[\frac{{{T}_{1}}}{{{T}_{2}}}=\sqrt{\frac{{{({{B}_{H}})}_{2}}}{{{({{B}_{H}})}_{1}}}}\] \[=\left[ \frac{1.5\times m}{3m} \right]\times 2\] \[=1\,m{{s}^{-1}}\]
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