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,

$\dfrac{m$A}{mB} = \dfrac{5}{1} \\[0.5em] \dfrac{KA}{KB} = \dfrac{125}{9}

Since,

$\dfrac{K$A}{KB} = \dfrac{\dfrac{1}{2}mAvA^2}{\dfrac{1}{2}mBvB^2} \\[0.5em] = \Big(\dfrac{mA}{mB}\Big) \times \Big(\dfrac{vA^2}{vB^2}\Big)

Substituting the values we get,

$\dfrac{125}{9} = \dfrac{5}{1} \times \dfrac{v$A^2}{vB^2} \\[0.5em] \Rightarrow \dfrac{vA^2}{vB^2} = \dfrac{125 \times 1}{9 \times 5} \\[0.5em] \Rightarrow \dfrac{vA}{vB} = \sqrt{\dfrac{25}{9}} = \dfrac{5}{3} \\[0.5em]

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