If a rod travels at a relativistic speed v , its mass

According to the special theory of relativity, the relativistic mass $m$ of an object moving with a velocity $v$ is given by the relation:

$m = \dfrac{m_0}{\sqrt{1 - \dfrac{v^2}{c^2}}}$

where $m_0$ is the rest mass of the object and $c$ is the speed of light in vacuum.

The Lorentz factor $\gamma$ is defined as:

$\gamma = \dfrac{1}{\sqrt{1 - \dfrac{v^2}{c^2}}}$

Substituting $\gamma$ into the mass equation, we get:

$m = \gamma m_0$

Since the rod is traveling at a relativistic speed $v$, the factor $\gamma > 1$. Therefore, the relativistic mass of the rod must increase by a factor of $\gamma$ irrespective of the direction of its motion.