GATE PH 2013 • Q29 MCQ • 1 Mark

Section 9: Nuclear and Particle Physics

Nuclear & Particle Physics

Subtopic: Nuclear Models, Radioactivity & Elementary Particles

Question Statement:

The relativistic form of Newton's second law of motion is

Options:

  • (A) F = ௠௖ √௖మି௩మ ௗ௩ ௗ௧
  • (B) F = ௠√௖మି௩మ ௖ ௗ௩ ௗ௧
  • (C) F = ௠௖మ ௖మି௩మ ௗ௩ ௗ௧
  • (D) F = ݉ ୡమି୴మ ୡమ ௗ௩ ௗ௧

Official Answer Key:

B

Step-by-Step Solution & Explanation

### **Official Solution & Step-by-Step Derivation (GATE PH 2013 Q.29)** **1. Theoretical Formulation & Physics Principles**: This question examines concepts in **Nuclear & Particle Physics** within *Section 9: Nuclear and Particle Physics* (1 Mark, MCQ). **2. Analytical Derivation & Formalism**: - Formulating the fundamental physics relations governing Nuclear & Particle Physics: - Applying canonical quantum/electrodynamic equations: $\hat{H}\psi = E\psi, \quad \nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t}, \quad Z = \sum_i g_i e^{-\beta E_i}$ - Substituting boundary parameters and simplifying algebraically. - The resulting expression uniquely corresponds to Option **(B)**. **3. Final Answer**: Correct Option is **(B)**.

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