A light and a heavy object have the same momentum. Find out the ratio of their kinetic energies. Which one has a larger kinetic energy?
Answers
Hello
According to the question, both objects have same momentum.
Momentum : p = mv
Let the mass of lighter object be m . Mass of heavier body be M . Also velocity of lighter body be v1 and velocity of heavier body be v2 . So momentum of lighter body = mv1 and momentum of heavier body = Mv2
Kinetic energy : 1/2 mv²
As we know about the mass i.e which one is heavier and which one is lighter Let us take out velocities from equation of momentum.
v1 = p/m
v2 = p/M
Now we will put the value of these velocity in the formula of kinetic energy.
Let kinetic energy of lighter body be KE1 and kinetic energy of heavier body be KE2 .
⇒ KE1 = 1/2 * m * ( p²/m² ) { v1² = p²/m² }
⇒ KE2 = 1/2 * M * (p²/M² )
From the above we can see clearly that KE1 is greater than KE2 that is kinetic energy of lighter object is greater than that of heavier object.
Hope It Helps
Explanation:
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