A symmetric top has principal moments of inertia I1 = I2 =
2𝛼
3 , I3 = 2𝛼
about a set of principal axes 1, 2, 3 respectively, passing through its center of
mass, where 𝛼 is a positive constant. There is no force acting on the body and
the angular speed of the body about the 3 -axis is 𝜔3 =
1
8 rad/s. With what
angular frequency in rad/s does the angular velocity vector 𝜔⃗⃗ 1 precess about the
3-axis?
Options:
(A) 2
(B) 3
(C) 5
(D) 7
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2023 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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