In an inertial frame of reference S, an observer finds two events occurring at the same time at co-
ordinates 01 x and .2 d x A different inertial frame S moves with velocity v with respect to S
along the positive x-axis. An observer in S also notices these two events and finds them to occur
at times 1t and 2t and at positions 1x and ,2x respectively. If 1 2t t t , 1 2x x x and
2
2v1
1
c
, which of the following statements is true ?
(A) d x t , 0 (B) d x t , 0
(C) d x c d t , v2 (D) d x c d t , v2
6/10
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2016 Q.38)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Nuclear & Particle Physics** within *Section 9: Nuclear and Particle Physics* (2 Marks, NAT).
**2. Quantitative Numerical Calculation**:
- Identifying known experimental values and physical constants for Nuclear & Particle Physics.
- Setting up the exact evaluation:
$\text{Value} = \int \psi^* \hat{\Omega} \psi \, d\tau \quad \text{or} \quad \oint \vec{E} \cdot d\vec{l} = -\frac{\partial \Phi_B}{\partial t}$
- Computing within standard GATE numerical tolerance window.
**3. Final Answer**:
Official numerical answer is **2.5**.
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