Same Momentum, But Who Has More Kinetic Energy?

$\huge K=\dfrac{p^2}{2m}∝\color{forestgreen}{\dfrac{1}{m}}$ $\color{goldenrod}{\text{Hence body with lighter mass will have greater K.E .}}$

Let M be the mass of heavier body and m be the mass of lighter body.
and V be the velocity of heavier body and v be the mass of lighter body.
So, MV=mv...........(V<v)
$\frac{V}{v}=\frac{m}{M}$

So, kinetic energy of heavier body= $\frac{MV^2}{2}$

So, kinetic energy of lighter body= $\frac{mv^2}{2}$

Ratio between heavier to lower= $\frac{Mm^2}{mM^2} = \frac{m}{M}$

As $\frac{m}{M}$ <1 , so lighter object has greater K.E.

$\large \text{KE} = \dfrac{\text{p}^2}{2\text{m}}$ $\large \text{KE} \propto \dfrac{1}{\text{m}}$ $\large \text{K.E}_{\text{ lighter body}} > \text{K.E}_{\text{heavier body}}$

momentum is linked with force, which is turn is directly proportional to mass F=ma Therefore, more mass, same momentum, slower acceleration.

kinetic energy is linked with Work, which in turn is directly proportional to displacement W=Fd Therefore, slower acceleration, less work, less kinetic energy.

Therefore the heavy object has less kinetic energy than the light object when they have the same momentum.

It is obvious :)