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Two bodies of masses $m$ and $4m$ are moving with equal linear momentum. The ratio of their kinetic energies is:

1. $1:4$
2. $4:1$
3. $1:1$
4. $1:2$

Correct answer: $4:1$

Solution

If both bodies have the same momentum $p$, then $K=\dfrac{p^2}{2m}$. So the body of mass $m$ has four times the kinetic energy of the body of mass $4m$. Therefore the ratio is $4:1$.

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