Question

One main scale division of a vernier caliper is equal to \( m \) units. If the \( m \) divisions of the main scale coincide with the \( (n + 1)^{\text{th}} \) division of the 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. \( \frac{m}{n(n+1)} \)

Hint:

Least count is the smallest measurement a device can accurately measure; it’s crucial for precision in scientific experiments.

Answer 1

The Correct Option is B

Step 1: {Comprehending the Vernier Caliper}
The least count of the vernier scale is calculated as: \[ LC = {Main Scale Division} - {Vernier Scale Division} \] Step 2: {Implementing the Specified Condition} 
Given that \( n \) main scale divisions are equivalent to \( (n+1) \) vernier scale divisions, the relationship is: \[ n \times MSD = (n+1) \times VSD \] Step 3: {Determining the Least Count} 
\[ VSD = \frac{n}{n+1} \times MSD \] \[ LC = MSD - VSD = m - \frac{n}{n+1} m \] \[ LC = m \left(1 - \frac{n}{n+1} \right) \] \[ LC = \frac{m}{n+1} \] Consequently, the correct option is (B)