A) 40 J
B) 60 J
C) 100 J
D) 140 J
Correct Answer: B
Solution :
Given: Mass of metal ball = 2 kg; Speed of metal ball \[({{v}_{1}})\] = 36 km/h = 10 m/s and mass of stationary ball = 3 kg. We know that common velocity after collision \[{{v}_{1}}=\] \[{{v}_{2}}=v\frac{{{m}_{1}}{{v}_{1}}+{{m}_{2}}{{v}_{2}}}{{{m}_{1}}+{{m}_{2}}}=\frac{(2\times 10)+(3\times 0)}{2+3}\] \[=\frac{20}{5}=4\,m\text{/}s.\] Therefore loss of energy \[=\left[ \frac{1}{2}{{m}_{1}}v_{1}^{2}+\frac{1}{2}{{m}_{2}}v_{2}^{2} \right]-\frac{1}{2}\times ({{m}_{1}}+{{m}_{2}})\] \[{{(v_{1}^{2}+v_{2}^{2})}^{2}}=\left[ \frac{1}{2}\times 2\times {{(10)}^{2}}+\frac{1}{2}\times 3\,{{(0)}^{2}} \right]\] \[-\frac{1}{2}\times (2+3)\,{{(4)}^{2}}=100-40=60\,J.\]
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