A bomb of mass 20 kg, initially at rest, explodes into two pieces of masses 8 kg and 12 kg. If the kinetic energy of the 8kg piece is 576 J, find the kinetic energy (in joules) of the 12 kg piece.

$\text{ Speed of the }8\mathrm{kg}\text{ piece, }{\mathrm{v}}_1=\sqrt{\frac{2{\mathrm{E}}_1}{{\mathrm{m}}_1}}=\sqrt{\frac{2\times 576}{8}}=12\mathrm{m}/\mathrm{s}$

Let the speed of the 12 kg piece be $v_2$ . Since there is no external force, applying the law of conservation of momentum,

${\mathrm{m}}_2{\mathrm{v}}_2={\mathrm{m}}_1{\mathrm{v}}_1$

Or 

$\mathrm{ }{\mathrm{v}}_2=\frac{{\mathrm{m}}_1{\mathrm{v}}_1}{{\mathrm{m}}_2}=\frac{8\times 12}{12}=8\mathrm{m}/\mathrm{s}$ 

Kinetic energy of the 12kg piece is  ${\mathrm{E}}_2=\frac{1}{2}{\mathrm{m}}_2{\mathrm{v}}_2^2=\frac{1}{2}\times 12\times (8{)}^2=384\mathrm{J}$