A particle of rest mass $m_{0}$ is moving with speed $c / 2$ . What is its momentum?

\frac{m_{0} c}{2}

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\frac{1}{\sqrt{3}} m_{0} c

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\frac{2}{\sqrt{3}} m_{0} c

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none of the above

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Solution

The correct option is C $\frac{1}{\sqrt{3}} m_{0} c$
We know that, mass of moving particle at velocity $m = \frac{m_{0}}{\sqrt{1 - {(\frac{v}{c})}^{2}}}$
since $, v = \frac{c}{2}$
$\Rightarrow m = \frac{2 m_{0}}{\sqrt{3}}$
$M o m e n t u m = m v = \frac{2 m_{0}}{\sqrt{3}} \frac{c}{2} = \frac{1}{\sqrt{3}} m_{0} c$

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