question_answer

If two bodies of masses 2m and m have their momenta in the ratio 8 : 1, then the ratio of their kinetic energies is _____.

Answer:

\[\frac{K{{E}_{1}}}{K{{E}_{2}}}={{\left( \frac{{{P}_{1}}}{{{P}_{2}}} \right)}^{2}}\times \frac{{{m}_{2}}}{{{m}_{1}}}\times \frac{8}{1}\times \frac{8}{1}=\frac{m}{2m}=\frac{32}{1}\] \[KE:K{{E}_{2}}=32:1\]