Calculating the Least Count of Vernier Calipers

Vernier calipers are widely used in scientific and industrial applications to measure objects with great accuracy. The least count of vernier calipers is an important factor that determines the precision of the instrument. Here are the steps to calculate the least count of vernier calipers:

Step 1: Determine the Main Scale Division

The main scale of a vernier caliper has n divisions per centimeter. To determine the main scale division, we need to measure the distance between two adjacent divisions on the main scale using a ruler. Let's say this distance is d cm.

Step 2: Determine the Vernier Scale Division

The vernier scale of a vernier caliper has n-1 divisions that coincide with n divisions of the main scale. To determine the vernier scale division, we need to measure the distance between two adjacent divisions on the vernier scale using a ruler. Let's say this distance is V cm.

Step 3: Calculate the Least Count

The least count of vernier calipers is given by the formula:

LC = d/n - V/(n-1)

where LC is the least count, d is the main scale division, n is the number of divisions per centimeter on the main scale, and V is the vernier scale division.

For example, if the main scale has 10 divisions per centimeter and the vernier scale has 9 divisions that coincide with 10 divisions of the main scale, then n=10 and n-1=9. Let's say the distance between two adjacent divisions on the main scale is 0.1 cm and the distance between two adjacent divisions on the vernier scale is 0.09 cm. Then, the least count of the vernier caliper is:

LC = 0.1/10 - 0.09/9 = 0.01 - 0.01 = 0.001 cm

Therefore, the least count of the vernier caliper is 0.001 cm.

Conclusion

The least count of vernier calipers is an important parameter that determines the accuracy and precision of the instrument. It can be calculated by determining the main scale division and the vernier scale division and using the formula LC = d/n - V/(n-1).