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?

  • Work and energy CBSE Class 9
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Answer

Linear momentum of first object, ๐‘1 = ๐‘š1๐‘ฃ1 and of second object, ๐‘2= ๐‘š2๐‘ฃ2

But, ๐‘1 = ๐‘2

or,ย  ย ๐‘š1๐‘ฃ1 = ๐‘š2๐‘ฃ2

If ๐‘š1 < ๐‘š2 then ๐‘ฃ1 > ๐‘ฃ2

(K.E.)1 = {1\over2}(๐‘š1๐‘ฃ1)๐‘ฃ1 = {1\over2}๐‘1๐‘ฃ1

and (K.E.)2 = {1\over2}(๐‘š2๐‘ฃ2)๐‘ฃ2 = {1\over2}๐‘2๐‘ฃ2

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, ๐‘ฃ1 > ๐‘ฃ2

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

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