For a body with mass $m$ and momentum $p$, the kinetic energy is $K = \frac{p^2}{2m}.$

Given that all three bodies have equal kinetic energies, we have $\frac{p^2}{2m} = \text{constant}.$ Therefore, $p^2 \propto m \quad \Rightarrow \quad p \propto \sqrt{m}.$

Masses are: $m_A = 400\,\text{g} = 0.4\,\text{kg}, \quad m_B = 1.2\,\text{kg}, \quad m_C = 1.6\,\text{kg}.$

Hence the ratio of momenta is $p_A : p_B : p_C = \sqrt{0.4} : \sqrt{1.2} : \sqrt{1.6}.$

Factor out $0.4$: $0.4 : 1.2 : 1.6 = 1 : 3 : 4.$ So, $\sqrt{0.4} : \sqrt{1.2} : \sqrt{1.6} = \sqrt{1} : \sqrt{3} : \sqrt{4} = 1 : \sqrt{3} : 2.$

Therefore, the correct option is: $\boxed{A \; : \; 1 : \sqrt{3} : 2}$