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  4. A 12 kg bomb at rest explodes into two pieces of 4 kg and 8 kg. If the momentum of 4 kg piece is 20 Ns, the kinetic energy of the 8 kg piece is

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Q. A $12\,kg$ bomb at rest explodes into two pieces of $4 \,kg$ and $8 \,kg$. If the momentum of $4\,kg$ piece is $20\,Ns$, the kinetic energy of the $8\,kg$ piece is

KCETKCET 2016Laws of Motion

Solution:

Key Idea Explosion causes internal forces so momentum of system is conserved.
$m=12 \,kg$
$u=0$ (rest)
Initial momentum $=m \times u=0$
Momentum of $4 \,kg$ piece $=20\, Ns$
$m_{1} \times v=20 $
$v=\frac{20}{4}=5 \,ms ^{-1}$
Applying conservation of momentum,
$0=m_{1} v+m_{2} v'=20+8 \times v'$
$v'=\frac{-20}{8}=\frac{-5}{2} ms ^{-1}$
After explosion,
Then, $KE =\frac{1}{2} m v^{2}$
$=\frac{1}{2} \times 8 \times\left(\frac{5}{2}\right)^{2}$
$=\frac{1}{2} \times 8 \times \frac{25}{4}=25 \,J$