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

Correct Answer: B

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