The pitch of a screw gauge is `0.5 mm` and there are `50` divisions on the circular scale. In measuring the thickness of a metal plate, there are five divisions on the pitch scale (or main scale) and thirty fourth divisions coincide with the reference line. Calculate the thickness of the metal plate.

Explanation

To calculate the thickness of the metal plate using the screw gauge, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Pitch of the screw gauge (P) = 0.5 mm
- Number of divisions on the circular scale (N) = 50
- Main scale reading (MSR) = 5 divisions
- Circular scale reading (CSR) = 34 divisions

2. **Calculate the Least Count (LC):**
The least count of the screw gauge can be calculated using the formula:
\[ \text{Least Count (LC)} = \frac{\text{Pitch}}{\text{Number of divisions on circular scale}} = \frac{0.5 \, \text{mm}}{50} = 0.01 \, \text{mm} \]

3. **Calculate the Main Scale Reading (MSR):**
The main scale reading can be calculated as:
\[ \text{MSR} = \text{Number of divisions on main scale} \times \text{Pitch} = 5 \times 0.5 \, \text{mm} = 2.5 \, \text{mm} \]

4. **Calculate the Circular Scale Reading Contribution:**
The contribution from the circular scale reading can be calculated as:
\[ \text{CSR Contribution} = \text{CSR} \times \text{Least Count} = 34 \times 0.01 \, \text{mm} = 0.34 \, \text{mm} \]

5. **Calculate the Total Thickness:**
The total thickness of the metal plate can be calculated by adding the main scale reading and the circular scale reading contribution:
\[ \text{Thickness} = \text{MSR} + \text{CSR Contribution} = 2.5 \, \text{mm} + 0.34 \, \text{mm} = 2.84 \, \text{mm} \]

### Final Answer:
The thickness of the metal plate is **2.84 mm**.

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