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Question

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?

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Answer

Linear momentum of first object, 𝑝1 = π‘š1𝑣1 and of second object, 𝑝2= π‘š2𝑣2

But, 𝑝1 = 𝑝2

or,Β  Β π‘š1𝑣1 = π‘š2𝑣2

If π‘š1 < π‘š2 then 𝑣1 > 𝑣2

(K.E.)1 = {1\over2}(π‘š1𝑣1)𝑣1 = {1\over2}𝑝1𝑣1

and (K.E.)2 = {1\over2}(π‘š2𝑣2)𝑣2 = {1\over2}𝑝2𝑣2

So, {({K.E.})_1}\over{({K.E.})_2} = {{1\over2}p_1v_1}\over{{1\over2}p_2v_2} = {v_1\over v_2}

But, 𝑣1 > 𝑣2

Therefore, (K.E.)1 > (K.E.)2

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