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  • 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?

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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Solution.

For any object of mass m, the kinetic energy and momentum are defined as:
KE=\frac{1}{2}mv^{2}
P=mv

Here v is the speed of the object.
We try to eliminate speed and to find out the relation between kinetic energy and momentum.
KE=\frac{1}{2}m\left ( \frac{p}{m} \right )^{2}
\Rightarrow KE=\frac{1}{2}\frac{p^{2}}{m}

If two bodies have the same momentum, then kinetic energy will be inversely proportional to the mass of the body.
Therefore, the lighter body will have more kinetic energy than the heavy body.

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