Question

In a vernier callipers, 50 vernier scale divisions are equal to 48 main scale divisions. If one main scale division = 0.05 mm, then the least count of the vernier callipers is ________ mm.

• A. 0.02
• B. 0.005
• C. 0.002
• D. 0.05

Hint:

Least count measures the smallest length an instrument can resolve accurately.

Answer 1

The Correct Option is C

To determine the least count of the vernier calipers, we need to understand the relationship between the main scale and the vernier scale. The problem states that:

• 50 vernier scale divisions are equal to 48 main scale divisions.

Also, one main scale division is given as 0.05 mm.

The formula to find the least count (\(LC\)) of the vernier calipers is:

\(LC = \text{Value of one main scale division} - \text{Value of one vernier scale division}\)

Let's calculate the value of one vernier scale division:

• Value of 50 vernier scale divisions (VSD) = 48 main scale divisions (MSD)
• Value of 1 VSD = \(\frac{48 \text{ MSD}}{50}\) = 0.96 MSD

Now we know that the value of one main scale division (MSD) is 0.05 mm, so:

• Value of 1 VSD in mm = 0.96 × 0.05 mm = 0.048 mm

Substitute these values into the formula for the least count:

\(LC = 0.05 \, \text{mm} - 0.048 \, \text{mm} = 0.002 \, \text{mm}\)

Thus, the least count of the vernier calipers is 0.002 mm.

Therefore, the correct answer is:

0.002