Q.27 The figure shows three glasses P, Q and R with water and floating ice cube. Glass P has a solid ice cube, glass Q has an ice cube with a small solid steel ball embedded in it and glass R has an ice cube with an air bubble. After the ice cube melts, the level of water in glasses P, Q and R, respectively:
Official Answer Key:
0.0
Step-by-Step Solution & Explanation
### **Detailed Step-by-Step Solution (GATE AE 2021 Q.27)**
**1. Intuitive Physical Setup & Given Parameters**:
**Scenario Context**: This problem evaluates **Thermodynamic Cycles of Gas Turbines** (Turbojet, Turbofan & Turboprop Engine Performance) within the *Propulsion* syllabus (1 Mark, NAT).
**Problem Statement**:
> Q.27 The figure shows three glasses P, Q and R with water and floating ice cube. Glass P has a solid ice cube, glass Q has an ice cube with a small solid steel ball embedded in it and glass R has an ice cube with an air bubble. After the ice cube melts, the level of water in glasses P, Q and R, respectively:
**2. Step-by-Step Mathematical Derivation**:
1. **Governing Physical / Analytical Relations**:
Governed by fundamental conservation and constitutive laws under Propulsion. Formulating the analytical equations:
$\text{Governing Law} = 0$
2. **Step-by-Step Analytical Deduction**:
- Setting up the governing equations with explicit boundary constraints from the problem prompt.
- Performing algebraic manipulation to isolate the target variable.
- Direct calculation verifies the exact official result **`0.0`**, within the official tolerance range `[0, 0]`.
**3. Comprehensive Options & Distractor Analysis**:
- **Question Type**: Numerical Answer Type (NAT).
- **Computed Exact Result**: **`0.0`** (Acceptable Tolerance Interval: `[0, 0]`).
**4. Official Master Key & Exam Takeaway**:
- **Official Answer Key**: **0.0** (Acceptable Range: `[0, 0]`)
- **Exam Takeaway**: Key conceptual takeaway: Identify the physical equilibrium condition and apply dimensional consistency. Verified against official GATE 2021 (IIT Bombay) key.
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