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Two bodies of different masses have the ...

Two bodies of different masses have the same momentum. Compare their kinetic energies.

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Let `K_1, p_1 and K_2,p_2` be the kinetic energies and momenta of the two bodies of masses `m_1 and m_2` , respectively.
Now, `K=1/2 mv^2 =(m^2v^2)/(2m) =(p_2)/(2m)`
`therefore K_1 =(p_1^2)/(2m_1), K_2= (p_2^2)/(2m_2)`
`therefore (K_1)/(K_2) =(m_2 p_1^2)/(m_1p_2^2) =(m_2)/(m_1) as p_1= p_2`
Hence, the body with the lighter mass has greater kinetic energy ,. i.e., the kinetic energy is inversely proportinal to the mass, if the momentum remains constant.
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