A stationary bomb explodes into two parts of masses 3 kg and 1 kg. The total KE of the two parts after explosion is 2400 J. The KE of the smaller part is:

${\mathrm{K}}_1+{\mathrm{K}}_2=2400 \left(i\right)$

$$\begin{gathered} {\mathrm{p}}_1={\mathrm{p}}_2 \\ \therefore \sqrt{2{\mathrm{K}}_1{\mathrm{m}}_1}=\sqrt{2{\mathrm{K}}_2{\mathrm{m}}_2} \\ \mathrm{or} \frac{{\mathrm{K}}_1}{{\mathrm{K}}_2}=\frac{{\mathrm{m}}_2}{{\mathrm{m}}_1}=\frac{3}{1} \left(\mathrm{ii}\right) \end{gathered}$$

Solving these two equations, we get:
${\mathrm{K}}_1 = \mathrm{Kinetic} \mathrm{energy} \mathrm{of} \mathrm{smaller} \mathrm{part}= 1800 \mathrm{J}$