Two bodies A and B have masses in the ratio 5:1 and their kinetic energies are in the ratio 125:9. Find the ratio of their velocities.

Given,

$$\begin{aligned}\frac{m_A}{m_B} = \frac{5}{1} \\[0.5em] \frac{K_A}{K_B} = \frac{125}{9}\end{aligned}$$

Since,

$$\begin{aligned}\frac{K_A}{K_B} = \frac{\frac{1}{2}m_Av_A^2}{\frac{1}{2}m_Bv_B^2} \\[0.5em] = \Big(\frac{m_A}{m_B}\Big) \times \Big(\frac{v_A^2}{v_B^2}\Big)\end{aligned}$$

Substituting the values we get,

$$\begin{aligned}\frac{125}{9} = \frac{5}{1} \times \frac{v_A^2}{v_B^2} \\[0.5em] \Rightarrow \frac{v_A^2}{v_B^2} = \frac{125 \times 1}{9 \times 5} \\[0.5em] \Rightarrow \frac{v_A}{v_B} = \sqrt{\frac{25}{9}} = \frac{5}{3} \\[0.5em]\end{aligned}$$

Hence, ratio between velocities of A and B is 5 : 3