question_answer

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

Answer:

                If \[{{\upsilon }_{1}}\] and \[{{\upsilon }_{2}}\] are the velocities of two bodies having masses \[{{m}_{1}}\] and \[{{m}_{2}}\]respectively, then \[{{m}_{1}}{{\upsilon }_{1}}={{m}_{2}}{{\upsilon }_{2}}\]               or \[m_{1}^{2}\upsilon _{1}^{2}=m_{2}^{2}\upsilon _{2}^{2}\] or            \[\frac{{{m}_{1}}\upsilon _{1}^{2}}{{{m}_{2}}\upsilon _{2}^{2}}=\frac{{{m}_{2}}}{{{m}_{1}}}\]     or \[\frac{({{m}_{1}}\upsilon _{1}^{2}/2)}{({{m}_{2}}\upsilon _{2}^{2}/2)}=\frac{{{m}_{2}}}{{{m}_{1}}}\] or            \[\frac{{{K}_{1}}}{{{K}_{2}}}=\frac{{{m}_{2}}}{{{m}_{1}}}\]