The main scale of vernier callipers reads in millmetre and its vernier is divided into 8 divisions, which coincide with 5 divisions of main scale . Then
When two jaws of instrument touch each other the zero of the vernier coincide with the zero of main scale . A rod is tightly placed along its length between both jaws, it is observed that the zero vernier scale lies just left to `36^("th")` division of main scale and fourth division of vernier scale coincide with the main scale. Then the measured value is

Options

A. 3.66 cm
B. 3.55 cm
C. 3.65 cm
D. 3.56 cm

Answer

To solve the problem step by step, we will follow the procedure outlined in the video transcript.

### Step 1: Determine the relationship between the vernier scale and the main scale.
The problem states that the vernier scale has 8 divisions that coincide with 5 divisions of the main scale.

**Calculation:**
1 Vernier Scale Division (VSD) = 5/8 Main Scale Division (MSD)

### Step 2: Calculate the least count of the vernier scale.
The least count (LC) of the vernier scale can be calculated using the formula:
\[ \text{Least Count} = 1 \text{ MSD} - 1 \text{ VSD} \]

Using the relationship from Step 1:
\[ \text{LC} = 1 \text{ MSD} - \frac{5}{8} \text{ MSD} = 1 - \frac{5}{8} = \frac{3}{8} \text{ MSD} \]

Since 1 MSD = 1 mm, the least count of the vernier scale is:
\[ \text{LC} = \frac{3}{8} \text{ mm} \]

### Step 3: Identify the main scale reading (MSR).
The problem states that the zero of the vernier scale lies just left of the 36th division of the main scale. This means the main scale reading is:
\[ \text{MSR} = 35 \text{ mm} \]

### Step 4: Identify the vernier scale reading (VSR).
The problem states that the 4th division of the vernier scale coincides with the main scale. Therefore, the vernier scale reading is:
\[ \text{VSR} = 4 \times \text{LC} = 4 \times \frac{3}{8} \text{ mm} = \frac{12}{8} \text{ mm} = 1.5 \text{ mm} \]

### Step 5: Calculate the total measured value.
The total measured value (R) can be calculated using the formula:
\[ R = \text{MSR} + \text{VSR} \]
Substituting the values we found:
\[ R = 35 \text{ mm} + 1.5 \text{ mm} = 36.5 \text{ mm} \]

### Final Answer:
The measured value is **36.5 mm**.

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