A) 1/2
B) 1/3
C) 1/4
D) 1/5
Correct Answer: B
Solution :
: Velocity of A after collision \[{{v}_{A}}=\frac{({{m}_{A}}-{{m}_{B}})}{({{m}_{A}}+{{m}_{B}})}{{u}_{1}}\]where\[{{u}_{1}}\]is initial velocity of A. Velocity of B after collision where B is at rest initially. \[{{v}_{B}}=\frac{2{{m}_{A}}}{{{m}_{A}}+{{m}_{B}}}{{u}_{1}}\] Since \[{{v}_{A}}=-{{v}_{B}}\]after collision \[\therefore \] \[\frac{({{m}_{A}}-{{m}_{B}})}{({{m}_{A}}+{{m}_{B}})}{{u}_{1}}=-\frac{2{{m}_{A}}}{({{m}_{A}}+{{m}_{B}})}{{u}_{1}}\] Or \[{{m}_{A}}-{{m}_{B}}=-2{{m}_{A}}\]or \[3{{m}_{A}}={{m}_{B}}\] Or \[\frac{{{m}_{A}}}{{{m}_{B}}}=\frac{1}{3}\]
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