question_answer

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

Answer:

\[KE=\frac{{{P}^{2}}}{2m}\Rightarrow P\propto \sqrt{KE\times m}\] \[\Rightarrow \frac{{{P}_{1}}}{{{P}_{2}}}=\sqrt{\frac{K{{E}_{1}}}{K{{E}_{2}}}\times \frac{{{m}_{1}}}{{{m}_{2}}}}\] \[\frac{{{P}_{1}}}{{{P}_{2}}}=\sqrt{\frac{8}{1}\times \frac{m}{2m}=\frac{2}{1}}\]