Question

One main scale division of a vernier caliper is equal to m units. If n^th division of main scale coincides with (n + 1)^th division of vernier scale,
the least count of the vernier caliper is:

• A. \(\frac{n}{n+1}\)
• B. \(\frac{m}{n+1}\)
• C. \(\frac{1}{n+1}\)
• D. \(\frac{m}{n(n+1)}\)

Answer 1

The Correct Option is B

Step 1: Relationship between main scale and vernier scale Given that:

\[ n \, \text{MSD} = (n + 1) \, \text{VSD}. \]

From this:

\[ 1 \, \text{VSD} = \frac{n}{n + 1} \, \text{MSD}. \]

Step 2: Least count formula The least count (L.C.) of a vernier caliper is given by:

\[ \text{L.C.} = 1 \, \text{MSD} - 1 \, \text{VSD}. \]

Substitute \( 1 \, \text{VSD} \) from Step 1:

\[ \text{L.C.} = m - m \left( \frac{n}{n + 1} \right). \]

Simplify:

\[ \text{L.C.} = m \left[ 1 - \frac{n}{n + 1} \right]. \]

\[ \text{L.C.} = m \left( \frac{n + 1 - n}{n + 1} \right). \]

\[ \text{L.C.} = \frac{m}{n + 1}. \]

Final Answer: \( \frac{m}{n + 1} \).