In a vernier callipers having 10 Vsd the vernier constant is 0.1 mm When the jaws are closed zero of varnier lies to the left of zero of main and 7th Vsd coincides with scale division when a cylinder is placed between the jaws the main scale reading was 7.7 cm and vernier scale read 8 division What is the diameter of the cylinder ?

Options

A. 78.1mm
B. 77.5mm
C. 77.8mm
D. 78.5mm

Explanation

To find the diameter of the cylinder using the given vernier calipers, we will follow these steps:

### Step 1: Understand the Zero Error
The zero error occurs when the zero of the vernier scale does not coincide with the zero of the main scale when the jaws are closed. In this case, the zero of the vernier scale is to the left of the zero of the main scale.

Given:
- 10 VSD (Vernier Scale Divisions)
- The 7th VSD coincides with the main scale.

To calculate the zero error:
- Zero error = (Vernier Scale Reading - Main Scale Reading) × Vernier Constant
- Here, the reading is -7 VSD (since it is to the left) and the Vernier Constant is 0.1 mm.

Zero Error = -7 × 0.1 mm = -0.7 mm

### Step 2: Convert Main Scale Reading to mm
The main scale reading (MSR) is given as 7.7 cm. We need to convert this to mm:
- 1 cm = 10 mm
- Therefore, 7.7 cm = 7.7 × 10 mm = 77 mm.

### Step 3: Calculate the Vernier Scale Reading
The vernier scale reading (VSR) is given as 8 divisions. To find the contribution of the vernier scale to the measurement:
- VSR = 8 VSD × Vernier Constant
- VSR = 8 × 0.1 mm = 0.8 mm.

### Step 4: Calculate the Actual Diameter of the Cylinder
Now we can find the actual diameter of the cylinder using the formula:
- Diameter = MSR + VSR - Zero Error

Substituting the values:
- Diameter = 77 mm + 0.8 mm - (-0.7 mm)
- Diameter = 77 mm + 0.8 mm + 0.7 mm
- Diameter = 77 mm + 1.5 mm = 78.5 mm.

### Final Answer
The diameter of the cylinder is **78.5 mm**.

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