A particle of mass m is free to move on a frictionless horizontal two dimensional
(r, š) plane, and is acted upon by a force F = -
k
2r3 rĢ with k being a
positive constant. If pr and pš are the generalised momenta corresponding to
r and š respectively, then what is the value of
dpr
dt ?
Options:
(A) pš
2 - 2mk
2mr3
(B) 2pš
2 - mk
mr3
(C) pš
2 - 2mk
mr3
(D) 2pš
2 - mk
2mr3
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2023 Q.42)**
**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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