Question

Ratio of masses of electrons moving with a velocity $0.9$ times of speed of light and $0.8$ times of speed of light respectively are:

• A. $\sqrt{\frac{19}{36}}$
• B. $\sqrt{\frac{64}{81}}$
• C. $\sqrt{\frac{81}{64}}$
• D. $\sqrt{\frac{36}{19}}$

Answer 1

The correct option is D $\sqrt{\frac{36}{19}}$

As we know,
$m_e^{{}^{\prime }}=\frac{m}{[[1-{\left(\frac{u_e}{c}\right)}^2]{]}^{1/2}}$
$m_e^{\prime }=\frac{mc}{[c^2-u^2{]}^{1/2}}$
$\therefore \frac{m^{{}^{\prime }}}{m^{\prime \prime }}=\sqrt{\frac{1-(0.8{)}^2}{1-(0.9{)}^2}}=\sqrt{\frac{36}{19}}$