The kinetic energy $K$ of a body is related to its linear momentum $p$ and mass $m$ by the formula $K = \frac{p^2}{2m}$. Given that the two bodies have equal kinetic energies ($K_1 = K_2$): $\frac{p_1^2}{2m_1} = \frac{p_2^2}{2m_2}$ $\frac{p_1^2}{p_2^2} = \frac{m_1}{m_2}$ Taking the square root on both sides: $\frac{p_1}{p_2} = \frac{\sqrt{m_1}}{\sqrt{m_2}}$ Thus, the ratio of their momenta $p_1 : p_2$ is equal to $\sqrt{m_1} : \sqrt{m_2}$.