A heavy body and a light body have same momentum. Which one of them has more kinetic energy and why?

Explanation

Light body will have more kinetic energy than the heavier one.
To prove: `K.E_(I) gt K.E_(II0`
Solution : Mass and velocity of the light body- `m_(1)`, `v_(1)`
Mass and Velocity of the heavier body `=m_(2)`, `v_(2)` i.e. `m_(1) lt m_(2)`
Given : Momentum of light body `=` Momentum of heavier body
i.e. `m_(1)v_(1)=m_(2)v_(2)=K` (constant)
`v_(1)=(K)/(m_(1))` , `v_(2)=(K)/(m_(2))`
`K.E_(I)=(1)/(2)m_(1)v_(1)^(2)=(1)/(2)m_(1)[(K)/(m_(1))]^(2)`
`K.E_(I)=(1)/(2)(K^(2))/(m_(1))`
`K.E_(II)=(1)/(2)m_(2)v_(2)^(2)=(1)/(2)m_(2)[(K)/(m_(2))]^(2)`
`K.E_(II)=(1)/(2)(K^(2))/(m_(2))`
`(K.E_(I))/(K.E_(II))=((K^(2))/(2m_(1)))/((K^(2))/(2m_(2)))=((1)/(m_(1)))/((1)/(m_(2)))=(m_(2))/(m_(1))gt1`
`(K.E_(I))/(K.E_(II))gt1implies :. K.E_(I)gtK.E_(II)`
Hence Proved.