1. Condition for keeping the wire length constant

When temperature increases by $\Delta T$, the wire tends to expand by thermal strain

$\epsilon_{\text{thermal}} = \alpha \Delta T$

To keep the length unchanged, an equal and opposite mechanical strain must be produced by applying pressure (compressive stress).

So,

$\epsilon_{\text{mechanical}} = \epsilon_{\text{thermal}}$

Using Young's modulus,

$Y = \frac{\text{stress}}{\text{strain}} \Rightarrow \text{stress} = Y \alpha \Delta T$

2. Substitute the given values

Given:

$Y = 2 \times 10^{11}\,\text{Pa}$ $\alpha = 1.1 \times 10^{-5}\,\text{K}^{-1}$ $\Delta T = 100^\circ C = 100\,\text{K}$

Therefore,

$\text{stress} = 2 \times 10^{11} \times 1.1 \times 10^{-5} \times 100$

$= 2 \times 10^{11} \times 1.1 \times 10^{-3}$

$= 2.2 \times 10^8\,\text{Pa}$

3. Interpretation

The pressure required at the ends to prevent expansion is equal to this compressive stress.

Hence,

$P = 2.2 \times 10^8\,\text{Pa}$

4. Option check

• A: $2.2 \times 10^8\,\text{Pa}$ ✅
• B: $2.2 \times 10^9\,\text{Pa}$ ❌
• C: $2.2 \times 10^7\,\text{Pa}$ ❌
• D: $2.2 \times 10^6\,\text{Pa}$ ❌

So the correct option is A.