a light body and aheavy body have same momentum. which one will have greater kinetic energy
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Answer:
Answer:According to the question, a light body and a heavy body have same momentum. Between this two bodies the light body will gain more kinetic energy than the heavy body. Because, greater the mass is equals to greater the gravitational force which resists the the velocity as well as the kinetic energy.
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Momentum is defined as Mass multiplied to velocity of the body.
Kinetic Energy is defined as the energy possessed by a moving body which is provided as 1/2 of mass multiplied to velocity squared.
Since there are a few common terms in between them, we can derive a relation out of them.
K.E. = 1/2 mv² ...(1)
P = mv ...(2)
Considering the Second Equation, we get:
⇒ P = mv
⇒ P² = m²v²
⇒ 1/2 P² = 1/2 m²v²
⇒ P²/2 = m ( 1/2 mv² )
⇒ P²/2m = 1/2 mv² = K.E.
Therefore Kinetic Energy is Momentum Squared divided by twice of Mass.
According to your question, Momentum is same between heavy body and a light body. Let us consider the mass of heavier body to be 'M' and that of lighter body to be 'm'.
⇒ K.E. of Heavier body = P²/2M
⇒ K.E. OF Lighter Body = P²/2m
Now since Momentum is constant we only consider the masses. Now we can see that,
⇒ K.E ∝ (1 / Mass)
This says that Momentum is inversely proportional to Mass of the body. Therefore heavier the mass, less is the K.E. value.
Hence lighter the mass more is the K.E. value.
Hence the lighter body will have more K.E. than the heavier body.
Hope it helped!