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Kinetic Energy and Momentum comparison

A light body and a heavy body have the same momentum which of the two bodies will have greater kinetic energy ?

Sumanta Das requested to explain the answer to this question.

Answer:

As we know,

The momentum of a body, P = mv whee m is the mass and v is the velocity

and Kinetic Energy of a body, E = (1/2) mv2

Since the velocity term comes twice in E, the lighter body will have greater KE

Alternately,

P = mv

P2 = m2v2

p2/2m = (1/2) mv2 = E

which shows that E is inversely proportion to mass for bodies with same momentum.

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