Two frames S (solid lines) and S′ (dashed lines) with common origin are shown in the
figure below. Frame S is inertial while S′ is rotating about the common z-axis. There is a
point mass fixed at P on the x-axis of the S frame. The magnitude of the centrifugal force
and the Coriolis force experienced by the mass in the S′ frame is Fcen and Fcor,
respectively. Which of the following options is correct for these forces?
Options:
(A) Fcen = 0 and Fcor = 0
(B) Fcen ≠ 0 and Fcor ≠ 0 and Fcen =
Fcor
2
(C) Fcen ≠ 0 and Fcor ≠ 0 and Fcen = 2Fcor
(D) Fcen ≠ 0 and Fcor ≠ 0 and Fcen = Fcor
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2026 Q.49)**
**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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