$A$ light and a heavy object have the same momentum. Find the ratio of their kinetic energies. Which one has a larger kinetic energy?

(A) Let the two objects have masses $m_1$ and $m_2$ such that $m_2 > m_1$. Let their common momentum be $p$.
The kinetic energy $K$ is related to momentum $p$ and mass $m$ by the formula $K = \frac{p^2}{2m}$.
For the first object (lighter),$K_1 = \frac{p^2}{2m_1}$.
For the second object (heavier),$K_2 = \frac{p^2}{2m_2}$.
The ratio of their kinetic energies is $\frac{K_1}{K_2} = \frac{p^2 / 2m_1}{p^2 / 2m_2} = \frac{m_2}{m_1}$.
Since $m_2 > m_1$,it follows that $\frac{m_2}{m_1} > 1$,which implies $K_1 > K_2$.
Therefore,the lighter object has a larger kinetic energy.