Q111 / 200 · NEET 2005 · Physics
A bomb of mass $30 \mathrm{~kg}$ at rest explodes into two pieces of masses $18 \mathrm{~kg}$ and 12 $\mathrm{kg}$. The velocity of $18 \mathrm{~kg}$ mass is $6 \mathrm{~ms}^{-1}$. The kinetic energy of the other mass is:
- A$324 \mathrm{~J}$
- Correct answerB$486 \mathrm{~J}$
- C$256 \mathrm{~J}$
- D$524 \mathrm{~J}$
Solution
According to law of conservation of conservation of angular moments
$\begin{aligned}
30 \times 0 & =18 \times 6+12 \times V \\
\Rightarrow V & =-9 \mathrm{~m} / \mathrm{s}
\end{aligned}$
Negative sign indicates that both fragments move in opposite direction.
$\begin{aligned}
\text {K.E. of } 12 \mathrm{~kg} & =\frac{1}{2} \mathrm{mv}^2 \\
& =\frac{1}{2} \times 12 \times 81 \\
& =486 \mathrm{~J}
\end{aligned}$
$\begin{aligned}
30 \times 0 & =18 \times 6+12 \times V \\
\Rightarrow V & =-9 \mathrm{~m} / \mathrm{s}
\end{aligned}$
Negative sign indicates that both fragments move in opposite direction.
$\begin{aligned}
\text {K.E. of } 12 \mathrm{~kg} & =\frac{1}{2} \mathrm{mv}^2 \\
& =\frac{1}{2} \times 12 \times 81 \\
& =486 \mathrm{~J}
\end{aligned}$Hence, the correct answer is option: 'B'.