Question Bank MCQ • 1 Mark Section 2: Classical Mechanics Special theory of relativity

QB_PH_053: Special theory of relativity

Question Statement

If the kinetic energy of a relativistic particle equals its rest energy ($K = m_0 c^2$), its relativistic momentum is:
(A) \sqrt{3} m_0 c
(B) m_0 c
(C) 2 m_0 c
(D) \frac{1}{2} m_0 c
Correct Answer
A
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: $E = 2 m_0 c^2 \implies E^2 = p^2 c^2 + m_0^2 c^4 \implies 4 m_0^2 c^4 = p^2 c^2 + m_0^2 c^4 \implies p = \sqrt{3} m_0 c$.
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