A) 256 J
B) 486 J
C) 524 J
D) 324 J
Correct Answer: B
Solution :
Key Idea: The linear momentum of exploding part will remain conserved. Applying conservation of linear momentum, we write, \[{{m}_{1}}{{u}_{1}}={{m}_{2}}{{u}_{2}}\] Here, \[{{m}_{1}}=18\,kg,\,{{m}_{2}}=12\,kg\] \[{{u}_{1}}=6\,m{{s}^{-1}},\,\,{{u}_{2}}=\,\,?\] \[\therefore 18\times 6=12\,{{u}_{2}}\] \[\Rightarrow {{u}_{2}}=\frac{18\times 6}{12}=9\,m{{s}^{-1}}\] Thus, kinetic energy of 12 kg mass \[{{K}_{2}}=\frac{1}{2}\,{{m}_{2}}u_{2}^{2}\] \[=\frac{1}{2}\times 12\times {{(9)}^{2}}\] \[=6\times 81\] = 486 J
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