The vernier constant of a vernier callipers is `0.1 mm` and it has a positive zero error of `0.04 cm`. While measuring diameter of a rod, the main scale reading is `1.2 cm` and `5th` vernier division is coinciding with any scale division. The correct diameter of the rod is

Options

A. `1.21 cm`
B. `1.21 mm`
C. `1.29 mm`
D. `1.29 cm`

Explanation

To find the correct diameter of the rod using the given information, we will follow these steps:

### Step 1: Understand the given values
- Vernier constant (least count) = 0.1 mm = 0.01 cm
- Positive zero error = 0.04 cm
- Main scale reading (MSR) = 1.2 cm
- Vernier scale reading (VSR) = 5th Vernier division coinciding with a main scale division

### Step 2: Calculate the Vernier Scale Reading
Since the 5th Vernier division is coinciding with a main scale division, we need to calculate the Vernier scale reading.
- Each Vernier division represents the value of the Vernier constant, which is 0.01 cm.
- Therefore, the Vernier scale reading for the 5th division is:
\[ \text{VSR} = 5 \times \text{Vernier constant} = 5 \times 0.01 \text{ cm} = 0.05 \text{ cm} \]

### Step 3: Calculate the observed reading
Now, we can calculate the observed reading (OR) using the formula:
\[ \text{OR} = \text{MSR} + \text{VSR} \]
Substituting the values we have:
\[ \text{OR} = 1.2 \text{ cm} + 0.05 \text{ cm} = 1.25 \text{ cm} \]

### Step 4: Adjust for zero error
Since we have a positive zero error, we need to subtract the zero error from the observed reading to get the correct reading:
\[ \text{Correct Reading} = \text{OR} - \text{Zero Error} \]
Substituting the values:
\[ \text{Correct Reading} = 1.25 \text{ cm} - 0.04 \text{ cm} = 1.21 \text{ cm} \]

### Conclusion
The correct diameter of the rod is:
\[ \text{Correct Diameter} = 1.21 \text{ cm} \]

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