A rod PQ of proper length L lies along the x-axis and moves towards the positive
x direction with speed v =
3c
5 with respect to the ground (see figure) , where
c is the speed of light in vacuum. An observer on the ground measures the
positions of P and Q at different times tP and tQ respectively in the ground
frame, and finds the difference betwen them to be
9L
10 . What is the value
of tQ - tP?
Options:
(A) L
3c
(B) L
5c
(C) L
6c
(D) 2L
3c
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2023 Q.40)**
**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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