Two bodies of masses $m_1$ and $m_2$ have equal kinetic energies. What is the ratio of their velocities?

Let the $v_1$ and $v_2$ be the velocities of the two bodies having masses $m_1$ and $m_2$ respectively.

Therefore $\frac{1}{2}m_1v_1^2$ and $\frac{1}{2}m_2v_2^2$ would be their kinetic energies.

But it is given that both the bodies have equal kinetic energies

Therefore, $\frac{1}{2}m_1v_1^2=\frac{1}{2}m_2v_2^2$

Or $m_1v_1^2=m_2v_2^2$

Or $\frac{v_1^2}{v_2^2}=\frac{m_2}{m_1}$

Or $\frac{v_1}{v_2}=\sqrt{\frac{m_2}{m_1}}$

Or $v_1:v_2=\sqrt{m_2}:\sqrt{m_1}$