Question

The velocity, \( v \), at which the mass of a particle is double its rest mass is:

• A. \( v = c \)
• B. \( v = \sqrt{3} c \)
• C. \( v = \sqrt{2} c \)
• D. \( v = 2c \)

Hint:

In relativity, the velocity at which the particle's mass doubles is given by \( v = \sqrt{3} c \), which is less than the speed of light.

Answer 1

The Correct Option is B

Step 1: Relativistic mass-energy relationship. The relativistic mass \( m \) of a particle is related to its velocity by the formula: \[ m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}} \] Where \( m_0 \) is the rest mass, \( v \) is the velocity, and \( c \) is the speed of light.
Step 2: Conclusion. For \( m = 2 m_0 \), solving the equation gives \( v = \sqrt{3} c \).