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The formula for momentum 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 = 1/2mv^2. Let the KE of the heavier body be KE1 and KE of the lighter object be KE2.
So, KE1/KE2= 1/2MV^2÷1/2mv^2
= MV^2/mv^2
= M/m× V^2/v^2
= v/V × V^2/v^2 [ from 1]
= 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.
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