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A light body and a heavy body have same linear momentum. Which one has greater Kinetic Energy?

Let P1 and P2 be the linear momentum and kinetic energy E1 and E2 of light and heavy body respectively.

According to question,
P1=P2
i.e., m1v1=m2v2
or, v2v1=m1m2 .......... (i)
Again,
E1=12m1v21
E2=12m2v22
or, E2E1=12m2v2212m1v21=m2m1(v2v1)2
or, m2m1(m1m2)2=m1m2

If m1 is mass of light body and m2 be the mass of heavy body. Then,
m1<m2, E2<E1
or, E1>E2 .......... (ii)
∴ From equation (ii) we conclude that, the lighter body has more Kinetic Energy.

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