Question

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

• A. 25 J
• B. 20 J
• C. 50 J
• D. 40 J

Answer 1

Answer: (A)

25 J

Answer 2

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, $KE =\frac{1}{2} m v^{2}$
$=\frac{1}{2} \times 8 \times\left(\frac{5}{2}\right)^{2}$
$=\frac{1}{2} \times 8 \times \frac{25}{4}=25 \,J$