Question

When a rod moves at a relativistic speed v, its mass

(a) must increase by a factor of γ
(b) may remain unchanged
(c) may increase by a factor other than γ
(d) may decrease

Answer 1

(a) must increase by a factor of γ

If a rod is moving at a relativistic speed v, its mass is given by

$m=\gamma m_o=\frac{m_o}{\sqrt{1-{\displaystyle \frac{v^2}{c^2}}}}$
Here,
$\gamma =\frac{1}{\sqrt{1-{\displaystyle \frac{v^2}{c^2}}}}$

Thus, its mass must increase by a factor of $\gamma$.