A light and a heavy object have the same momentum. Which one has greater kinetic energy?         RAS(mains)2016

The formula for momentum(गति) of a body is

P= MV

Now let the mass and velocity of the heavy body be M and V respectively. The mass and velocity of the of the lighter object be m and v respectively.

So , P/P= MV/mv

Since the momentum(p)is same we get,

MV=mv

M/m= v/V…………….(1)

The formula for kinetic energy is,

KE = 1/2 m v² . Let the KE of the heavier body be KE1 and KE of the lighter object be KE2.

So, KE1/KE2=1/2 M V²   ÷   1/2 m v²

=>KE1/KE2= M V² / m v²

=>KE1/KE2= M/m× V²/ v²

=>KE1/KE2= v/V × V²/ v²    [ from 1]

=>KE1/KE2= V/v

So, KE1/KE2= V /v

Now, as the velocity of the lighter object is greater, since its mass is less, the kinetic energy of the lighter object will be greater.

Another explanation could be:

 kinetic energy is the energy possessed by a body due to its motion, so the body with more velocity will have greater kinetic energy.