A particle of mass 1 kg is released from a height of 1 m above the ground. When
it reaches the ground, what is the value of Hamilton's action for this motion in J s?
(g is the acceleration due to gravity; take gravitation potential to be zero on the
ground)
Options:
(A) - 2
3 ඥ2g
(B) 5
3 ඥ2g
(C) 3ඥ2g
(D) - 1
3 ඥ2g
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2022 Q.41)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Nuclear & Particle Physics** within *Section 9: Nuclear and Particle Physics* (2 Marks, 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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