Question

In a Vernier caliper, \(N+1\)  divisions of vernier scale coincide with  \(N\) divisions of main scale. If 1 MSD represents 0.1 mm, the vernier constant (in cm) is:

• A. \(\frac{1}{10N}\)
• B. \(\frac{1}{100(N+1)}\)
• C. \(100N\)
• D. \(10N+1\)

Answer 1

The Correct Option is B

Calculating the Vernier Constant (V.C.)

Step 1: Formula for the Vernier Constant (V.C.) 

The Vernier constant is given by:

V.C. = Value of 1 MSD − Value of 1 VSD

Step 2: Relate MSD and VSD values

If (N + 1) VSDs coincide with N MSDs, then:

Value of 1 VSD = Value of 1 MSD × (N / (N + 1))

Step 3: Substitute Values and Simplify

Now substitute the values:

V.C. = 0.1mm − 0.1mm × (N / (N + 1))

V.C. = 0.1 / (N + 1) mm

Quick Tip

To convert to centimeters, use:

V.C. = 1 / 100(N + 1) cm

Answer 2

Calculating the Vernier Constant (V.C.)

Step 1: Formula for the Vernier Constant (V.C.) 

The Vernier constant is given by:

V.C. = Value of 1 MSD − Value of 1 VSD

Step 2: Relate MSD and VSD values

If (N + 1) VSDs coincide with N MSDs, then:

Value of 1 VSD = Value of 1 MSD × (N / (N + 1))

Step 3: Substitute Values and Simplify

Now substitute the values:

V.C. = 0.1mm − 0.1mm × (N / (N + 1))

V.C. = 0.1 / (N + 1) mm

Quick Tip

To convert to centimeters, use:

V.C. = 1 / 100(N + 1) cm