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Kinetic Energy

A proton and ...

Question

A proton and a deuteron have kinetic energies in the ratio 1 : 2. The ratio of their linear momentum is

1 : \sqrt{2}

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\sqrt{2} : 1

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2:1

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1:2

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Solution

The correct option is D 1:2
$K_{p} / K_{d} = (P_{p}^{2} / 2 m_{p}) / (P_{d}^{2} / 2 m_{d})$ .
Now, $K_{p} / K_{d} = 1 / 2$ and $m_{d} = 2 m_{p}$ Using them on the above equation, Ratio of their linear momentum will be 1/2.

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