In a vernier calipers 1 M.S.D = 0.1 cm and the least count is 0.05 mm . If the reading on this vernier calipers while taking a measurement is 2.8 mm, then the vernier coinciding divison is ______.

Options

A. 20
B. 4
C. 8
D. 16

Answer

To solve the problem, we need to find the Vernier Coinciding Division (VCD) using the information provided about the Vernier calipers. Let's break it down step by step.

### Step 1: Understand the given values
- **Main Scale Division (M.S.D)** = 0.1 cm = 1 mm
- **Least Count (L.C)** = 0.05 mm
- **Reading on the Vernier Caliper (Vernier Scale Reading)** = 2.8 mm

### Step 2: Identify the Main Scale Reading (M.S.R)
The main scale reading is the whole number part of the Vernier scale reading. Since the reading is 2.8 mm, the main scale reading (M.S.R) is:
- M.S.R = 2 mm (the whole number part of 2.8 mm)

### Step 3: Calculate the remaining part for VCD
To find the Vernier Coinciding Division (VCD), we need to subtract the M.S.R from the Vernier Scale Reading:
- Remaining part = Vernier Scale Reading - M.S.R
- Remaining part = 2.8 mm - 2 mm = 0.8 mm

### Step 4: Use the formula to find VCD
The formula relating the Vernier Scale Reading is:
\[ \text{Vernier Scale Reading} = \text{M.S.R} + (\text{VCD} \times \text{Least Count}) \]

Rearranging this gives us:
\[ \text{VCD} = \frac{\text{Vernier Scale Reading} - \text{M.S.R}}{\text{Least Count}} \]

Substituting the values we have:
\[ \text{VCD} = \frac{0.8 \text{ mm}}{0.05 \text{ mm}} \]

### Step 5: Calculate VCD
Now, performing the division:
\[ \text{VCD} = \frac{0.8}{0.05} = 16 \]

### Conclusion
The Vernier Coinciding Division (VCD) is **16**.