Question

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

Answer 1

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