Question

100 Vernier scale divisions match with 99 main scale divisions of a slide caliper. If the value of each main scale division is 1 mm, then the Vernier constant is:

• A. 1 mm
• B. 100 µm
• C. 10 µm
• D. 1 µm

Hint:

The Vernier constant is calculated by dividing the length of one main scale division by the number of Vernier scale divisions.

Answer 1

The Correct Option is C

Step 1: Recall the shortcut formula for Vernier constant.
When N Vernier divisions span (N-1) main scale divisions, the Vernier constant simplifies to:
\[ \text{VC} = \frac{1\,\text{MSD}}{N} \]

Step 2: Check why this shortcut works.
Each Vernier division is shorter than 1 MSD by a fraction \( \frac{1}{N} \) of an MSD, since N of them together are missing exactly one full MSD compared to N main scale divisions. That missing sliver, spread evenly over N divisions, is what the Vernier constant measures.

Step 3: Plug in the numbers.
Here \( N = 100 \) and 1 MSD = 1 mm:
\[ \text{VC} = \frac{1\,\text{mm}}{100} = 0.01\,\text{mm} \]

Step 4: Convert to micrometers and state the Final Answer.
\[ 0.01\,\text{mm} = 10\,\mu\text{m} \]
\[ \boxed{\text{VC} = 10\,\mu\text{m}} \]

Answer 2

Working through a real measurement helps make sense of what the Vernier constant physically represents, rather than just plugging numbers into a formula.

1. 1 mm: Imagine lining up the caliper's jaws with nothing between them (a zero reading). If the least count were 1 mm, the Vernier scale would only ever let you read whole millimeters, exactly what the main scale already shows on its own.
2. 100 µm: At this least count, ten Vernier readings would be needed to cover the gap that this caliper actually covers in just one, since its Vernier scale is finer than that.
3. 10 µm: Picture sliding the Vernier scale along until its first division lines up with a main scale mark. Because 100 Vernier divisions are squeezed into a span that would normally hold 99 main scale divisions, each small slide of the Vernier scale by one division shifts the matching mark by just 0.01 mm relative to the main scale. That tiny shift, 10 micrometers, is the smallest length the caliper can distinguish.
4. 1 µm: This resolution would only show up if the caliper's Vernier scale were ten times finer than the one described, cramming a thousand divisions into 999 main scale divisions instead of a hundred into 99.

The size of that leftover sliver between one main scale division and one Vernier division is exactly what defines the Vernier constant, and for this caliper it works out to 10 micrometers.

The correct answer is 10 µm.