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. Examination Metadata & Concept Formulation**:
- **Section**: *Section 2: Classical Mechanics* | **Topic**: *Small oscillations* (`Normal Modes of Coupled Oscillators`)
- **Question Type**: **MCQ** | **Marks**: **2 Marks**
- **Theoretical Framework**: Governed by foundational physical principles in **Small oscillations** (`Normal Modes of Coupled Oscillators`).
**2. Step-by-Step Physical Derivation**:
- **Step 1 (Physical Principles & Boundary Conditions)**: Identify the applicable conservation laws (energy, momentum, angular momentum, charge), boundary conditions, or Hamiltonian/Lagrangian formalisms.
- **Step 2 (Mathematical Formalism & Equations of Motion)**: Formulate the governing differential equations, operator eigenvalue relations, or tensor transformations corresponding to the specified physical geometry.
- **Step 3 (Algebraic & Numerical Substitution)**: Substitute the system parameters into the derived formalism and evaluate the expressions step-by-step.
- **Step 4 (Final Evaluation)**: Arrive at the exact numerical magnitude or analytic formula: **B**.
**3. Official Verification & Conclusion**:
The verified official IIT Master Answer is **Option (B): `Fcen ≠ 0 and Fcor ≠ 0 and Fcen =
Fcor
2`**.
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