Question

If the speed of a rod moving at a relativistic speed parallel to its length is doubled,

• A. the length will become half of the original value
• B. the mass will become double of the original value
• C. the length will decrease
• D. the mass will increase

Answer 1

Answer: (C), (D)

The correct options are
C the length will decrease
D the mass will increase

Let the rest mass and rest length of the rod be $m_o$ and $L_o$, respectively.

According to relativity, length of the moving object parallel to its motion (or velocity) gets reduced by a factor of $\sqrt{1-\frac{v^2}{c^2}}$ of its rest length but its mass gets increased by the same factor.

$\therefore$ Parallel length of the moving object $L_{\parallel }=L_o\sqrt{1-\frac{v^2}{c^2}}$ $⟹L_{\parallel }<L_o$

Also mass of the moving object $m=\frac{m_o}{\sqrt{1-\frac{v^2}{c^2}}}$ $⟹m>m_o$

Hence options C and D are correct.