Subtopic: Wave Mechanics, Operators & Perturbation Theory
Question Statement:
A symmetric rigid body has moment of inertia I1, I2, I3 about its principal axes 1, 2, and
3, respectively, with I1 = I3 = I⊥ and I2 ≠ I⊥. It is rotating in space with no torque on it
so that its angular momentum L⃗ is constant. Let 𝜔1, 𝜔2, 𝜔3 be the components of its
angular velocity along the principal axes 1, 2, and 3, respectively. Which of the following
quantities is/are constant during the motion of this rigid body?
Options:
(A) 𝜔1 + 𝜔3
(B) 𝜔1
2 + 𝜔3
2
(C) Angle between axis 2 and L⃗
(D) 𝜔2
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2026 Q.55)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Quantum Mechanics** within *Section 4: Quantum Mechanics* (2 Marks, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Quantum Mechanics:
- 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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