A solid rod is just fits between two walls having gap of 2m. If the temperature increases by 50°C then the thermal stress developed in Gap is? Given that, `Y = 3 xx 10^(11) N//m^(2), alpha = 2 xx 10^(-4)// ""^(@)C`

Explanation

To solve the problem of thermal stress developed in a solid rod when the temperature increases, we can follow these steps:

### Step 1: Understand the parameters given
- **Gap between walls (L)** = 2 m
- **Temperature increase (ΔT)** = 50 °C
- **Young's modulus (Y)** = \(3 \times 10^{11} \, \text{N/m}^2\)
- **Coefficient of linear expansion (α)** = \(2 \times 10^{-4} \, \text{°C}^{-1}\)

### Step 2: Identify the formula for thermal stress
The formula for thermal stress (σ) in a solid rod is given by:

\[ \sigma = Y \cdot \alpha \cdot \Delta T \]

Where:
- σ = thermal stress
- Y = Young's modulus
- α = coefficient of linear expansion
- ΔT = change in temperature

### Step 3: Substitute the values into the formula
Now, we will substitute the known values into the formula:

\[ \sigma = (3 \times 10^{11} \, \text{N/m}^2) \cdot (2 \times 10^{-4} \, \text{°C}^{-1}) \cdot (50 \, \text{°C}) \]

### Step 4: Calculate the thermal stress
Now, we perform the multiplication step by step:

1. Calculate \( \alpha \cdot \Delta T \):
\[ 2 \times 10^{-4} \cdot 50 = 0.01 \]

2. Now, multiply by Young's modulus:
\[ \sigma = 3 \times 10^{11} \cdot 0.01 = 3 \times 10^{9} \, \text{N/m}^2 \]

### Final Answer
The thermal stress developed in the gap is:
\[ \sigma = 3 \times 10^{9} \, \text{Pa} \]