A) + 0.5nysand+ 0.3 m/s
B) - 0.5 m/s and + 0.3 m/s
C) + 0.3 m/s and - 0.5 m/s
D) - 0.3 m/s and + 0.5 m/s
Correct Answer: D
Solution :
Key Idea: Momentum and energy both are conserved in elastic collision. Given, \[{{v}_{A}}=+0.5\,m/s,\,{{v}_{B}}=-0.3\,m/s\] Initial momentum = final momentum \[{{m}_{A}}{{v}_{B}}+{{m}_{B}}={{m}_{A}}v{{}_{A}}+{{m}_{B}}v{{}_{B}}\] \[\Rightarrow \] \[0.5+(-0.3)=v{{}_{A}}+v{{}_{B}}\] ?.. (i) From law of conservation of energy, \[\frac{1}{2}({{m}_{A}}\,v_{A}^{2}+{{m}_{B}}\,v_{B}^{2})=\frac{1}{2}({{m}_{A}}\,v_{A}^{2}+{{m}_{B}}v_{B}^{2})\] ?.. (ii) \[{{(0.5)}^{2}}+{{(-0.3)}^{2}}=v_{A}^{2}+v_{B}^{2}\] From Eqs. (i) and (ii), we get \[v{{}_{A}}=-0.3\,m/s,\,v{{}_{B}}=+0.5\,m/s\]. Note: In an elastic collision, velocities after collision get interchanged.
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