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  Solved  Paper-2006

A) 144 J     

B)                        288 J                     

C)        192 J                     

D)        96 J

Correct Answer: B

Solution :

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 \[=\frac{4\times {{(12)}^{2}}}{2}=288\,J\]