A bimetallic strip is formed out of two identical strips one of copper and the other of brass. The temperature of the strip goes up by `DeltaT`and the strip bends to from an arc of radius of curvature R. Then R is.

Options

A. proportional to `DeltaT`
B. inversely proportional to `DeltaT`
C. proportional to `|alpha_B-alpha_C|`
D. inversely proportional to `|alpha_B-alpha_C|`

Explanation

To solve the problem regarding the bimetallic strip made of copper and brass, we need to analyze how the radius of curvature \( R \) relates to the change in temperature \( \Delta T \) and the coefficients of linear expansion of the two metals.

### Step-by-Step Solution:

1. **Understand the Bimetallic Strip**: A bimetallic strip consists of two different metals bonded together. When the temperature changes, each metal expands by different amounts due to their different coefficients of linear expansion.

2. **Define Coefficients of Linear Expansion**: Let \( \alpha_C \) be the coefficient of linear expansion for copper and \( \alpha_B \) be the coefficient of linear expansion for brass.

3. **Change in Length**: When the temperature increases by \( \Delta T \), the change in length for each metal can be expressed as:
- For copper: \( \Delta L_C = L \alpha_C \Delta T \)
- For brass: \( \Delta L_B = L \alpha_B \Delta T \)

4. **Bending of the Strip**: The difference in expansion causes the strip to bend. The curvature of the strip is related to the difference in expansion between the two metals.

5. **Radius of Curvature Formula**: The radius of curvature \( R \) of the bimetallic strip is given by the formula:
\[ R = \frac{d}{|\alpha_B - \alpha_C| \Delta T} \]
where \( d \) is the thickness of the strip.

6. **Analyze the Proportionality**:
- From the formula, we see that \( R \) is inversely proportional to \( |\alpha_B - \alpha_C| \) and \( \Delta T \).
- This means that as \( \Delta T \) increases, \( R \) decreases, and as the difference in coefficients \( |\alpha_B - \alpha_C| \) increases, \( R \) also decreases.

7. **Conclusion**: Therefore, we conclude that:
- \( R \) is inversely proportional to \( \Delta T \).
- \( R \) is also inversely proportional to \( |\alpha_B - \alpha_C| \).

### Final Answer:
- \( R \) is inversely proportional to \( |\alpha_B - \alpha_C| \) and \( \Delta T \).