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. (a)`L_1 gtL_2 gtL_3`
B. (b)`L_3 gt L_1 gtL_2`
C. (c)`L_2 gt L_3 gtL_1`
D. (d)`L_1 =L_2 =L_3`

Answer

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

### Step-by-Step Solution:

1. **Understanding the Behavior of Brass with Temperature:**
- Brass, like most materials, expands when heated and contracts when cooled. This means that as the temperature increases, the length of the brass scale increases.

2. **Identifying the Readings:**
- At room temperature, the reading of the brass scale is denoted as \( L_1 \).
- When the temperature is above room temperature, the reading is \( L_2 \).
- When the temperature is below room temperature, the reading is \( L_3 \).

3. **Analyzing the Readings:**
- Since the brass scale expands with an increase in temperature, the reading at a temperature above room temperature (\( L_2 \)) will be greater than the reading at room temperature (\( L_1 \)).
- Conversely, when the temperature is below room temperature, the brass scale contracts, leading to a reading (\( L_3 \)) that is greater than the reading at room temperature (\( L_1 \)) but less than the reading at a higher temperature (\( L_2 \)).

4. **Establishing the Relationship:**
- From the above analysis, we can conclude:
- \( L_3 > L_1 \) (reading below room temperature is greater than at room temperature)
- \( L_1 < L_2 \) (reading at room temperature is less than reading above room temperature)
- Therefore, we can establish the overall relationship:
- \( L_3 > L_1 < L_2 \)

5. **Final Relation:**
- The final relation can be summarized as:
- \( L_3 > L_1 < L_2 \) or \( L_3 > L_2 \) (since \( L_2 \) is the highest reading).

### Conclusion:
The correct relation between the readings is \( L_3 > L_1 < L_2 \).