Question

A light body and heavy body have equal kinetic energy, which one have greater momentum?

Answer 1

Let the masses be MM and mm where M>mM>m. Since their KEs are equal, it follows: 

                            12Mv21=12mv2212Mv12=12mv22
where v1v1 is the velocity of the heavier body and v2v2 that of the lighter body. From the above relation, we have,

                           Mm=v22v21Mm=v22v12

or,                       v2v1=Mm−−√v2v1=Mm

Since, M>m, v2>v1v2>v1. It then immediately follows that 

                            mv2Mv1=mM−−√mv2Mv1=mM

Since M>m, mM<1mM<1 and hence mv2<Mv1mv2<Mv1.