question_answer

Two bodies of masses \[{{m}_{1}}\] and \[{{m}_{2}}\] have equal kinetic energies. What is the ratio of their linear momenta?

Answer:

                Given that \[\frac{1}{2}{{m}_{1}}\upsilon _{1}^{2}=\frac{1}{2}{{m}_{2}}\upsilon _{2}^{2}\]                 or            \[\frac{{{\upsilon }_{1}}}{{{\upsilon }_{2}}}=\sqrt{\frac{{{m}_{2}}}{{{m}_{1}}}}\]                 or            \[\frac{{{m}_{1}}{{\upsilon }_{1}}}{{{m}_{2}}{{\upsilon }_{2}}}=\frac{{{m}_{1}}}{{{m}_{2}}}\sqrt{\frac{{{m}_{2}}}{{{m}_{1}}}}=\sqrt{\frac{{{m}_{1}}}{{{m}_{2}}}}\]                 or            \[\frac{{{p}_{1}}}{{{p}_{2}}}=\frac{\sqrt{{{m}_{1}}}}{\sqrt{{{m}_{2}}}}\]