A body of mass 8kg and another of mass 2kg are moving with equal...

Given: The mass of the objects ${m}_{1} = 8kg$ and ${m}_{2} = 2kg$.

Let the momentum of the $8kg$ and $2kg$ masses is ${p}_{1}$ and ${p}_{2}$, respectively, then according to question, their kinetic energy are equal, i.e.,

${K}_{1} = {K}_{2}$

${p}_{1}^{2}2{m}_{1} = {p}_{2}^{2}2{m}_{2}$

$\dfrac{{p}_{1}}{{p}_{2}} = \sqrt{\dfrac{{m}_{1}}{{m}_{2}}} = \sqrt{\dfrac{4}{1}} = \dfrac{2}{1}$