Question

The energy \( E \) and momentum \( p \) of a moving body of mass \( m \) are related by some equation. Given that \( c \) represents the speed of light, identify the correct equation:

• A. \( E^2 = p^2 c^2 + m^2 c^4 \)
• B. \( E^2 = p^2 c^2 + m^2 c^4 \)
• C. \( E^2 = p c^2 + m^2 c^2 \)
• D. \( E^2 = p c^2 + m^4 c^4 \)

Hint:

The energy-momentum relation \( E^2 = p^2 c^2 + m^2 c^4 \) is a fundamental result in special relativity that relates a particle's energy to its momentum and rest mass.

Answer 1

The Correct Option is A

The energy-momentum relation for a relativistic particle is given by the famous equation:

\[ E^2 = p^2 c^2 + m^2 c^4, \]

where:

• \( E \) is the total energy of the particle,
• \( p \) is the momentum of the particle,
• \( c \) is the speed of light in a vacuum,
• \( m \) is the rest mass of the particle.

This equation is derived from the special theory of relativity and relates the energy of a particle to both its momentum and its rest mass.

Final Answer: \( E^2 = p^2 c^2 + m^2 c^4 \).