Question

A vernier caliper having least count \(\frac{1}{20N}\)cm and one main scale division is 1 mm, then value of one vernier scale division is

• A. \(\frac{N+1}{2N}mm\)
• B. \(\frac{2N+1}{2N}mm\)
• C. \(\frac{2N-1}{2N}mm\)
• D. \(\frac{2N+2}{2N}mm\)

Answer 1

The Correct Option is C

To find the value of one vernier scale division, we will use the concept of a vernier caliper. A vernier caliper is a precision instrument used to measure length with great accuracy. It consists of a main scale and a vernier scale.

The relationship between the least count, main scale division, and vernier scale division can be expressed as:

\[ \text{Least Count (LC)} = \text{Value of 1 main scale division (MSD)} - \text{Value of 1 vernier scale division (VSD)} \]

From the given data:

• Least Count, \text{LC} = \frac{1}{20N} \text{ cm} = \frac{1}{200N} \text{ mm} \text{ (since 1 cm = 10 mm)}
• The main scale division (MSD) is 1 \text{ mm}.

Substitute these values into the formula for the least count:

\[ \frac{1}{200N} = 1 - \text{VSD} \]

Solving for the vernier scale division (VSD):

\[ \text{VSD} = 1 - \frac{1}{200N} \] \[ \text{VSD} = \frac{200N}{200N} - \frac{1}{200N} \] \[ \text{VSD} = \frac{200N - 1}{200N} \] \[ \text{VSD} = \frac{2N - 1}{2N} \text{ mm} \]

Thus, the value of one vernier scale division is \frac{2N-1}{2N} \text{ mm}. Therefore, the correct answer is:

• \(\frac{2N-1}{2N}\text{ mm}\)