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

Answer 2

Step 1: Understand the relation between energy and momentum.
The energy \( E \) and momentum \( p \) of a moving body are related through an equation derived from special relativity. The total energy \( E \) of a moving body consists of its rest energy and the kinetic energy, and the momentum \( p \) is related to the velocity of the body.

Step 2: The equation for energy and momentum.
The relativistic energy-momentum relation is given by the equation:
\[ E^2 = p^2 c^2 + m^2 c^4, \] where:
- \( E \) is the total energy of the body,
- \( p \) is the relativistic momentum,
- \( m \) is the rest mass of the body,
- \( c \) is the speed of light in a vacuum.
This equation connects the total energy, momentum, and rest mass of an object in motion.

Step 3: Explanation of the terms.
- The term \( p^2 c^2 \) represents the contribution to the total energy from the object's momentum.
- The term \( m^2 c^4 \) represents the rest energy of the object (when the object is at rest, \( p = 0 \)).

Final Answer:
The correct equation relating the energy \( E \) and momentum \( p \) of a moving body of mass \( m \) is:
\[ E^2 = p^2 c^2 + m^2 c^4. \]