Introduction:
When two unequal masses have the same momentum, it can be proven that the heavier body possesses lesser kinetic energy. This can be explained by understanding the concepts of momentum and kinetic energy, and their relationship to mass.

Momentum:
Momentum is defined as the product of an object's mass and its velocity. Mathematically, momentum (p) can be represented as p = m * v, where m is the mass and v is the velocity of the object. Momentum is a vector quantity, meaning it has both magnitude and direction.

Kinetic Energy:
Kinetic energy is defined as the energy possessed by an object due to its motion. Mathematically, kinetic energy (KE) can be represented as KE = (1/2) * m * v^2, where m is the mass and v is the velocity of the object. Kinetic energy is a scalar quantity, meaning it only has magnitude.

Proof:
To prove that the heavier body possesses lesser kinetic energy when two unequal masses have the same momentum, we can assume two masses, m1 and m2, with m1 > m2 and equal momenta, p1 = p2.

Step 1: Equating Momenta:
Given p1 = p2, we can write m1 * v1 = m2 * v2, where v1 and v2 are the velocities of the two masses.

Step 2: Rearranging the Equation:
Dividing both sides of the equation by m1 and m2 respectively, we get v1 = (m2/m1) * v2.

Step 3: Substituting the Value of v1:
Substituting the value of v1 in the equation for kinetic energy, we have KE1 = (1/2) * m1 * (m2/m1)^2 * v2^2.

Step 4: Simplifying the Equation:
Simplifying the equation, we get KE1 = (1/2) * m2^2/m1 * v2^2.

Step 5: Comparing Kinetic Energies:
Since m1 > m2, the term m2^2/m1 is less than 1. Therefore, KE1 < ke2,="" indicating="" that="" the="" heavier="" body="" possesses="" lesser="" kinetic="" />

Conclusion:
In conclusion, when two unequal masses have the same momentum, the heavier body possesses lesser kinetic energy. This can be proven mathematically by equating the momenta of the two masses and comparing their kinetic energy equations.

It is an potential energy due to velocity