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Question

A bomb of 12 kg explodes into two pieces of masses 4 kg and 8 kg. The velocity of 8kg mass is 6 m/sec. The kinetic energy of the other mass is

Moderate

A

48 J
B

32 J
C

24 J
D

288 J

Solution

As the initial momentum of bomb was zero, therefore after explosion two parts should possess numerically equal momentum
i.e. $m_{A} v_{A} = m_{B} v_{B} \Rightarrow 4 \times v_{A} = 8 \times 6 \Rightarrow v_{A} = 12 m / s$
$∴$ Kinetic energy of other mass A, = $\frac{1}{2} m_{A} v_{A}^{2}$
$= \frac{1}{2} \times 4 \times {(12)}^{2} = 288 J$

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