The coefficient of linear expansion of a rod is `alpha` and its length is L. The increase in temperature required to increase its legnth by 1% is

Options

A. `1/(alpha)`
B. `1/(10 alpha)`
C. `1/(50 alpha)`
D. `1/(100 alpha)`

Answer

To solve the problem, we need to determine the increase in temperature required to increase the length of a rod by 1% given its coefficient of linear expansion, denoted as \( \alpha \), and its original length \( L \).

### Step-by-Step Solution:

1. **Understand the Concept of Linear Expansion**:
The change in length (\( \Delta L \)) of a rod due to a change in temperature (\( \Delta T \)) is given by the formula:
\[ \Delta L = \alpha L \Delta T \]
where:
- \( \alpha \) is the coefficient of linear expansion,
- \( L \) is the original length of the rod,
- \( \Delta T \) is the change in temperature.

2. **Identify the Change in Length**:
We are told that the length of the rod increases by 1%. This means:
\[ \Delta L = 0.01 L \]

3. **Set Up the Equation**:
Substitute \( \Delta L \) into the linear expansion formula:
\[ 0.01 L = \alpha L \Delta T \]

4. **Simplify the Equation**:
We can cancel \( L \) from both sides (assuming \( L \neq 0 \)):
\[ 0.01 = \alpha \Delta T \]

5. **Solve for \( \Delta T \)**:
Rearranging the equation to find \( \Delta T \):
\[ \Delta T = \frac{0.01}{\alpha} \]

6. **Final Result**:
The increase in temperature required to increase the length of the rod by 1% is:
\[ \Delta T = \frac{1}{100 \alpha} \]