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