Calculate a particles kinetic energy if the rest energy of the particle is E and it is traveling at a speed of $\frac{12}{13} c$ .

\frac{7}{169} E

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\frac{5}{13} E

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\frac{3}{5} E

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\frac{8}{5} E

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\frac{13}{5} E

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Solution

The correct option is D $\frac{8}{5} E$
The total energy of a particle with speed $v$ and rest mass energy $E$ is $\frac{E}{\sqrt{1 - (\frac{v}{c})^{2}}}$ .
Hence, the kinetic energy of the particle $=$ Total energy $-$ Rest mass energy
$= \frac{E}{\sqrt{1 - (\frac{v}{c})^{2}}} - E$
For, $v = \frac{12}{13} c$ .
Kinetic energy of the particle $= \frac{8}{5} E$

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