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  4. A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be:

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Q. A body of mass $8 \,kg$ and another of mass $2 \, kg$ are moving with equal kinetic energy. The ratio of their respective momenta will be:

JEE MainJEE Main 2022Work, Energy and Power

Solution:

$ K . E =\frac{ P ^2}{2 m } $
$ K _1=\frac{ P _1^2}{2(8)} ; K _2=\frac{ P _2^2}{2(2)} $
$ K _1= K _2 $
So, $ 4 P _2^2= P _1^2$
$\frac{ P _1}{ P _2}=2$