The reading of brass scale at room temperature is `L_1` . Above room temperature reading is `L_2` and below room temperature reading is `L_3` . Then , relation between the readings is

Options

A. `L_1 gtL_2 gtL_3`
B. `L_3 gt L_1 gtL_2`
C. `L_2 gt L_3 gtL_1`
D. `L_1 =L_2 =L_3`

Answer

To solve the problem, we need to analyze how the length readings of a brass scale change with temperature variations.

### Step-by-Step Solution:

1. **Understanding the Properties of Brass**:
- Brass is a metal that expands when heated and contracts when cooled. This property is known as thermal expansion.

2. **Reading at Room Temperature**:
- Let the reading of the brass scale at room temperature be denoted as \( L_1 \).

3. **Reading Above Room Temperature**:
- When the temperature increases (above room temperature), the brass scale expands. As a result, the actual length of the scale increases, but the reading on the scale will be less than the actual length due to the expansion. We denote this reading as \( L_2 \).

4. **Reading Below Room Temperature**:
- Conversely, when the temperature decreases (below room temperature), the brass scale contracts. The reading on the scale will be more than the actual length because the scale is shorter than it would be at room temperature. We denote this reading as \( L_3 \).

5. **Establishing the Relationships**:
- From the above points, we can establish the following relationships:
- Since \( L_2 \) (above room temperature) is less than \( L_1 \) (room temperature), we have \( L_2 < L_1 \).
- Since \( L_3 \) (below room temperature) is greater than \( L_1 \), we have \( L_3 > L_1 \).

6. **Final Relation**:
- Combining these relationships, we can summarize:
- \( L_3 > L_1 > L_2 \)

### Conclusion:
Thus, the relationship between the readings is:
\[ L_3 > L_1 > L_2 \]