When a strip made or iron `(alpha_(1))` and copper `(alpha_(2)),(alpha_(2) gt alpha_(1))` is heated

Options

A. its length does not change
B. it gets twisted
C. it bends with iron on concave side
D. it bends with iron on convex side

Answer

To solve the problem of what happens when a strip made of iron and copper is heated, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We have a strip made of two different metals: iron (with coefficient of linear expansion \( \alpha_1 \)) and copper (with coefficient of linear expansion \( \alpha_2 \)). We know that \( \alpha_2 > \alpha_1 \), meaning copper expands more than iron when heated.

2. **Define the Coefficients of Linear Expansion**: The coefficient of linear expansion (\( \alpha \)) is defined as the fractional change in length per degree change in temperature. For a given length \( L \) and temperature change \( \Delta T \), the change in length \( \Delta L \) can be expressed as:
\[ \Delta L = \alpha L \Delta T \]

3. **Apply the Concept to Each Metal**:
- For copper, the change in length when heated is:
\[ \Delta L_{\text{copper}} = \alpha_2 L \Delta T \]
- For iron, the change in length when heated is:
\[ \Delta L_{\text{iron}} = \alpha_1 L \Delta T \]

4. **Compare the Changes in Length**: Since \( \alpha_2 > \alpha_1 \), we can conclude:
\[ \Delta L_{\text{copper}} > \Delta L_{\text{iron}} \]
This means that copper will expand more than iron when the strip is heated.

5. **Determine the Effect on the Strip**: Because copper expands more than iron, the strip will bend. The side with the greater expansion (copper) will push outward, while the side with less expansion (iron) will not extend as much.

6. **Identify the Direction of Bending**: The bending will occur such that the iron side will be on the concave side (the inside of the bend) and the copper side will be on the convex side (the outside of the bend). Thus, the strip will bend with iron on the concave side and copper on the convex side.

7. **Conclusion**: Therefore, the correct statement regarding the behavior of the strip when heated is that it bends with iron on the concave side.

### Final Answer:
The strip bends with iron on the concave side.

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