A) + 4 m/s for both
B) - 3m/s and + 5 m/s
C) - 4 m/s and + 4 m/s
D) - 5 m/s and + 3 m/s
Correct Answer: D
Solution :
Key Idea: In an elastic collision, linear momentum remains conserved. Given: \[{{u}_{1}}=3\,m/s,\,{{u}_{2}}=-5m/s,\,{{m}_{1}}={{m}_{2}}=m\] According to principle of conservation of linear momentum \[{{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}={{m}_{1}}{{v}_{1}}+{{m}_{2}}{{v}_{2}}\] \[m\times 3-m\times 5=m{{v}_{1}}+m{{v}_{2}}\] or \[{{v}_{1}}+{{v}_{2}}=-2\] ...(i) In an elastic collision, \[e=\frac{{{v}_{2}}-{{v}_{1}}}{{{u}_{1}}-{{u}_{2}}}\] \[\Rightarrow {{v}_{2}}-{{v}_{1}}=e\,({{u}_{1}}-{{u}_{2}})\] \[\Rightarrow {{v}_{2}}-{{v}_{1}}=(1)\,(3+5)\]\[(\because \,e=1)\] \[\Rightarrow {{v}_{1}}-{{v}_{2}}=-8\] ...(ii) Adding Eqs. (i) and (ii), we obtain \[2{{v}_{1}}=-\,10\,\] \[\Rightarrow {{v}_{1}}=-5\,m/s\] From Eq. (i), \[{{v}_{2}}=-2-{{v}_{1}}=-2+5=3\,m/s\] Thus, \[{{v}_{1}}=-5m/s\,,\,{{v}_{2}}=+3\,m/s\] Alternative: If two bodies collide elastically, then their velocities are interchanged. Since, it is an elastic collision hence, velocities after collision will be -5 m/s and 3 m/s.
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