Question

When the mass of an electron becomes equal to thrice its rest mass, its speed is- (where $c$-is the speed of light)

• A. $\frac{2}{3}c$
• B. $\frac{2\sqrt{2}}{3}c$
• C. $\frac{1}{3}c$
• D. $\frac{1}{4}c$

Answer 1

The correct option is B $\frac{2\sqrt{2}}{3}c$

Using the rest-mass relation,

$m=\frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}[\because \text{given}m=3m_0]$

$3m_0=\frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}$

$\Rightarrow 1-\frac{v^2}{c^2}=\frac{1}{9}$

$\Rightarrow 1-\frac{1}{9}=\frac{v^2}{c^2}$

$\Rightarrow \sqrt{\frac{8}{9}}=\frac{v}{c}$

$v=\frac{2\sqrt{2}}{3}c$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.