• # question_answer A bomb of mass 16 kg at rest explodes into two pieces of masses 4 kg and 12 kg. The velocity of the 12 kg mass is$4\text{ }m{{s}^{-1}}$. The kinetic energy of the other mass is                [AIEEE 2006] A) 144 J B) 288 J C) 192 J D) 96 J

Solution :

 [b] Here, momentum of the system is remaining conserved as external force is acting on the bomb (system). Initial momentum (before explosion) = Final momentum (after explosion) Let velocity of 4 kg mass be v m/s. From momentum conservation, we can say that its direction is opposite to velocity of 12 kg mass. From           ${{\vec{P}}_{i}}={{\vec{P}}_{f}}$ $\Rightarrow$ $0=12\times 4-4\times v$ $\Rightarrow$ $v=12\,m/s$ KE of 4kg mass $=\frac{4\times {{(12)}^{2}}}{2}=288\,J$

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