A light object and a heavy object have the same kinetic energy. Which has the greater momentum? Explain.

\[\begin{aligned}P_{L}=m_{L}v_{L}\\ P_{H}=m_{H}v_{H}\\ \dfrac {1}{2}m_{L}v^{2}_{L}=\dfrac {1}{2}m_{H}v^{2}_{H}\\ m_{L}v^{2}_{L}=m_{H}v^{2}_{H}\\ v^{2}_{L}=\dfrac {m_{H}}{m_{L}}v^{2}_{H}\\ v_{L}=\sqrt {\dfrac {m_{H}}{m_{L}}}v_{H}\\ m_{H} >m_{L}\\ SO,\sqrt {\dfrac {m_{H}}{m_{L}}} >1\\ P_{L}=m_{L}\left( \sqrt {\dfrac {m_{H}}{m_{L}}}v_{H}\right) \\ P_{L}=\sqrt {\dfrac {m_{L}.m_{L}.m_{H}}{m_{L}}}\times \left( v_{H}\right) \\ P_{L}=\sqrt {m_{L}m_{H}}\times \left( v_{H}\right) \\ P_{L}=\sqrt {m_{L}m_{H}}\times \left( \dfrac {m_{H}}{m_{H}}\right) \times \left( v_{H}\right) \\ P_{L}=\sqrt {\dfrac {m_{L}m_{H}}{m_{H}m_{H}}}\times \left( m_{H}\right) \times \left( v_{H}\right) \\ P_{L}=\sqrt {\dfrac {m_{L}}{m_{H}}}\times \left( m_{H}v_{H}\right) \\ P_{L}=\sqrt {\dfrac {m_{L}}{m_{H}}}P_{H}\\ m_{L} <m_{H}\\ SO,\sqrt {\dfrac {m_{L}}{m_{H}}} <1\\ \therefore P_{L} <P_{H}\end{aligned}\]

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