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A proton is moving at a speed much less than the speed of light. It has kinetic energy $K_{1}$ and momentum $p_{1}$ . If the momentum of the proton is doubled, so $p_{2} = 2 p_{1}$ , how is its new kinetic energy $K_{2}$ related to $K_{1}$ ?

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$K_{2} = K_{1}$

$K_{2} = 2 K_{1}$

$K_{2} = 3 K_{1}$

$K_{2} = 4 K_{1}$

answer is D.

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Detailed Solution

$K = \frac{p^{2}}{2 m}$ or $K \propto p^{2}$
If momentum is doubled, kinetic energy becomes four times.

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