A) \[\frac{2J}{p}-1\]
B) \[\frac{J}{p}+1\]
C) \[\frac{J}{p}-1\]
D) \[\frac{J}{2p}-1\]
Correct Answer: B
Solution :
Coefficient of restitution, \[e=\frac{{{v}_{2}}-{{v}_{1}}}{{{u}_{1}}-{{u}_{2}}}\] Here both the bodies are identical i.e., have the same mass, \[\therefore \]\[e=\frac{m{{v}_{2}}-m{{v}_{1}}}{m{{u}_{1}}-m{{u}_{2}}}\]\[=\frac{p{{'}_{2}}-p_{1}^{'}}{{{p}_{1}}-{{p}_{2}}}\] \[{{p}_{1}}=p\](Initial momentum of first body), \[{{p}_{2}}=\]Initial momentum of second body) = 0 (\[\because \] Final momentum \[{{p}_{2}}'=p+J\]) (\[\therefore \]Impulse = change in momentum) \[p_{1}^{'}=0\] (\[\because \] When two bodies of equal masses collide elastically, then they exchange their velocities) \[\therefore \]\[e=\frac{p+J}{p}\] \[=1+\frac{J}{p}\]
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