Question

An electron moves with a speed of $\frac{\sqrt{3}}{2}c$. Then its mass becomes_____ times its rest mass. (Given velocity of light $=c$)

• A. $2$
• B. $3$
• C. $3/2$
• D. $4$

Answer 1

The correct option is A $2$

Mass of on electron moving with speed $V$ is $\frac{m_o}{\sqrt{1-\frac{v^2}{c^2}}}$
where, $m_o$ is rest mass
$V$ is speed of electron
$C$ is speed of light
So, $m$ $=\frac{m_o}{\sqrt{1-\frac{v^2}{c^2}}}$
$=\frac{m_o}{\sqrt{1-\frac{{\left(\frac{\sqrt{3C}}{2}\right)}^2}{C^2}}}$
$=\frac{m_o}{\sqrt{1-\frac{3}{4}}}$
$=\frac{m_o}{\sqrt{\frac{1}{4}}}$
$=\frac{m_o}{\frac{1}{2}}$
$=2m_o$
So, mass becomes 2 times of its rest mass.