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, So, \[e=\frac{m{{v}_{2}}-m{{v}_{1}}}{m{{v}_{1}}-{{\mu }_{2}}}\] \[=\frac{{{P}_{2}}-{{P}_{1}}}{{{p}_{1}}-{{p}_{2}}}\] \[{{p}_{1}}=p\] (Intial 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 thy exchange then velocities) \[\therefore \] \[e=\frac{p+J}{p}\] \[=1+\frac{J}{p}\]
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