A) 140 J
B) 100 J
C) 60 J
D) 40 J
Correct Answer: C
Solution :
Key Idea: The first key idea is that final velocity v is given by the law of conservation of momentum. Initial momentum = Final momentum \[\therefore \] \[{{m}_{1}}{{v}_{1}}+{{m}_{2}}{{v}_{2}}=({{m}_{1}}+{{m}_{2}})v\] Given: \[{{v}_{1}}=36km/h=36\times \frac{5}{18}=10m/s\] \[{{v}_{2}}=0\] \[{{m}_{1}}=2kg,\] \[{{m}_{2}}=3kg\] \[\therefore \] \[v=\frac{{{m}_{1}}{{v}_{1}}+{{m}_{2}}{{v}_{2}}}{{{m}_{1}}+{{m}_{2}}}\] \[=\frac{2\times 10+3\times 0}{2+3}\] or \[v=\frac{20}{5}=5m/s\] Loss in kinetic energy \[=\frac{1}{2}{{m}_{1}}v_{1}^{2}+\frac{1}{2}{{m}_{2}}v_{2}^{2}-\frac{1}{2}({{m}_{1}}+{{m}_{2}}){{v}^{2}}\] \[=\frac{1}{2}\times 2\times {{(10)}^{2}}+0-\frac{1}{2}(2+3)\times {{(4)}^{2}}\] \[=100-40=60J\]
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